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AMERICAN MACHINISTS' HANDBOOK
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PUDLISH£RS OF BOOKS F O B^
Coal Age ^ Electric Railway Journal
Electrical World v Engineering. News-Record
American Machinist v The Contractor
Engineering 8 Mining Journal ^ Power
Metallurgical 6 Chemical Engineering
Electrical Merchandising
American Machinists* Handbook
AND '
DICTIONARY OF SHOP TERMS
A REFERENCE BOOK OF MACHINE SHOP AND
DRAWING ROOM DATA, METHODS AND
DEFINITIONS
BY
FRED H. COLVIN
Member American Society of Mechanical Engineers and Franklin Institute
Associate editor of the American Machinist, Author of " Machine
Shop Arithmetic," "Machine Shop Calculations"
"American Machinists' Grinding Book,"
" The Hill Kink Books," etc., etc.
and;
FRANK A. STANLEY
Member American Society of Mechanical Engineers and Franklin Institute
Associate editor of the American Machinist, Author of " Accurate
Tool Work," "Automatic Screw Machines," "American
Machinists' Grinding Book," " The Hill
Kink Books," etc.
SECOND EDITION
THOROUGHLY REVISED AND ENLARGED
FOURTEENTH IMPRESSION
TOTAL ISSUE, 147,000
McGRAW-HILL BOOK COMPANY, Inc.
239 WEST 39TH STREET. NEW YORK
LONDON: HILL PUBLISHING CO., Ltd.
6 & 8 BOUVERIE ST., E. C.
1914
Copyright, 1914, by the McGraw-Hill Book Company, Inc.
Copyright, 1908, by the Hill Publishing Company
All rights reserved
FIRST EDITION
First Printing, October, 1908
Second Printing, February, 1909
Third Printing, May, 1909
Fourth. Printing, November, 1909
Fifth Printing, April, 1910
Sixth Printing, October, 19 10
Seventh Printing, March, 1911
Eighth Printing, November. 191:^
Ninth Printing, May, 19 12
Tenth Printing, December, 191a
Eleventh Printing, April, 19 13
Total Issue, 36,000
SECOND EDITION
First Printing, July, 19 14
Second Printing, December, 19x4;
Third Printing, October, 1915
Fourth Printing, March, 19 16
Fifth Printing, June, 19 16
Sixth Printing, October, 1916
Seventh Printing, March, 1917
Eighth Printing, June, 19 17 •
Ninth Printing, October, 19 17
Tenth Printing, December, 1917
Eleventh Printing, March, 1918
Twelfth Printing, May, 1918
Thirteenth Printing, September, 191?
Fourteenth Prmting, January, 1919
Total Issue, 111,000
C 6 i"^
PREFACE TO SECOND EDITION
Ever since the first printing of this book, the authors have been
studying waj^s and means of making it better, and the addition of
one hundred and sixty pages by no means gives an adequate idea
of the extent to which it has been revised.
Each section has been carefully studied to make it cover the
changed and changing conditions of shop and drawing-room work
in the hope of making it even more valuable than before.
Many of the changes have been due to suggestions made by users
of the Handbook, and we shall appreciate a continuance of their
interest and assistance in pointing out possibilities of improvement.
The Authors.
PREFACE TO THE FIRST EDITION
Every man engaged in mechanical work of any kind, regardless
of his position in the shop or drawing room, frequently requires
information that is seldom remembered and is not usually available
when wanted.
With this in mind it has been our endeavor to present in con-
venient form such data as will be of value to practical men in the
various branches of machine work. While some of the matter in-
cluded may seem elementary, it was considered necessary in order
to make the work complete. Much of the information has never
before been available to the mechanic without tiresome search and
consultation.
We believe that the Dictionary section will be found of service
to the younger mechanics and in helping to estabHsh standard names
for various parts which are now more or less confused in different
sections of the coimtry.
Our indebtedness to various manufacturers and individuals is
hereby acknowledged, and in the back of the book will be found a
list of such authorities with page references to the information fur-
nished by them.
We dare not hope that no errors will be found and we shall be glad
to have them pointed out and to receive any suggestions as to addi-
tions or other changes which may add to the value of the book.
The Authors.
CONTENTS
SCREW THREADS
Cutting Screw Threads
Page
Stud and Lead Screw Gears on Lathe i
Examples in Finding Gears in Screw Cutting i
Cutting Fractional Threads i
Diagram of Simple and Compound Gearing . 2
Condensed Rules for Screw Cutting 3
Gears for Screw Cutting 3
Following Motion of a Train of Gears 4
Effect of Compound Gearing in the Train 4
A Screw Thread Angle Table 4
Side Clearance of Tool for Thread Helix 4
Formulas for Finding the Angle of Clearance 5
Use of Protractor in Securing Tool Side Clearance .... 6
Multiple Thread Cutting 6
Table of Distances to Move Carriage in Multiple Thread
Cutting 7
Opening and Closing the Lead Screw Nut 7
Face-plate for Multiple Thread Cutting 8
Cutting Diametral Pitch Worms in the Lathe 8
Table of Change Gears for Diametral Pitch Worms ... 9
Examples in Finding Gears for Worm Cutting 10
The Brown & Sharpe 29-deg. Worm Thread and the Acme
29-deg. Standard Screw Thread 10
Full Size Sections of B. & S. Worm and Acme Screw
Threads, i in. pitch 11
Measurement of V-Tools 11
Gear Tooth Caliper as Used for Thread Measurements . . 12
Table for V-Tool Angle Measurements 13
Grinding the Flat on Thread Tools 13
Table of Grinding Flats on Tools for U. S. Form of Thread . 14-15
•
Standard Proportions of Screw Threads
Table of U. S. Standard Screw Threads 16
Table of Sharp "V" Screw Threads 17
Table of Whitworth Standard Screw Threads 18
Table of British Association Screw Threads 19
Table of French (Metric) Standard Screw Threads .... 20
Table of International Standard Screw Threads 21
International Standard Threads 21
Table of German Loewenherz Threads for Accurate Work. 22
viii CONTENTS
Page
Rolled Threads 23
Dimensions of Blanks for U. S. S. Rolled Thread Screws . 23
Table of Acme 29-deg. Screw Threads 24
Table of Acme 29-deg. Tap Threads 25
Measuring Screw Threads
Brown & Sharpe Screw Thread Micrometer Readings for
U. S. Threads ' . . 26
Brown & Sharpe Screw Thread Micrometer Readings for
Sharp "V" Threads 27
Brown & Sharpe Screw Thread Micrometer Readings for
Whitworth Threads ; 28
Explanation of Screw Thread Micrometer Caliper .... 28
Measuring Thread Diameters with Micrometers and Wires 29
Measuring Threads of Special Diameter 29
Formulas for U. S. Thread Measurement with Micrometers
and Wires 30
Table for U. S. Thread Measurement with Micrometer and
Wires 31
Formulas for Sharp "V" Measurement with Micrometers
and Wires 32
Table for Sharp "V" Measurement with Micrometers and
Wires 33
Watch Screw Threads 33
Formulas for Whitworth Thread Measurement with Mi-
crometers and Wires 34
Table for Whitworth Screw Measurement with Microm-
eters and Wires 35
Measuring Fine Pitch Screw Threads with Micrometers
and Wires 36
Constants for 3-wire and Micrometer System of Screw
Thread Measurement 36
Measuring Metric Threads with Micrometers and Wires 37
Constants for 3-wire and Micrometer System of Screw
Thread Measurement 37
Measuring Acme 29-deg. Threads 38
]\Ieasuring Brown & Sharpe 29-deg. Worm Threads 39
Table of Wire Sizes for Measuring B. & S. Worm Threads . . 39
Brown & Sharpe 29-deg. Worm Thread Formulas 40
Table of Brown & Sharpe 29-deg. Worm Thread Parts ... 40
Table of Wire Sizes for Measuring Acme 29-deg. Screw and
Tap Threads ' 40
Worm Wheel Hobs 41
PIPE AND PIPE THREADS
Briggs Standard Pipe Threads 42
Taper of Pipe End and Form of Pipe End in Briggs System 42
Longitudinal Section of Pipe Thread 42
CONTENTS ix
Page
Dimensions of Wrought Iron Welded Tubes, Briggs Stand-
ard 43
Table of British Standard Pipe Threads 44
Table of Tap Drills for Pipe Threads 45
Table of Metric Pipe Threads ' . . 45
The Pipe Joint in the Briggs Standard 46
Relation of Reamer, Tap, Die and Gages in Briggs System 46
Forming the Joint in the Briggs System 47
Table of Briggs Pipe Threads 47-48
Gage Sets for Briggs Pipe and Fittings 49
Relation and AppHcation of the Gages 49
National Standard Hose Coupling 50
TWIST DRILLS AND TAPS
Angle of Spiral 51
Clearance or Relief 51
Grooves for Best Results 51
Grinding or Sharpening 52
Angle of Clearance 52
High-speed DrilHng 53
Feeds and Speeds for Various Materials 53
Data for Drilhng Cast Iron 54
Horsepower Required to Drill Cast Iron 54
Drill Troubles and Pointers 55
Special Drills and Their Uses 55-56
Standard Types of Drills 57
Sizes of Drills, Decimal Equivalent and Letter 58-60
Tap Drill Sizes for Regular Threads 62
Tap Drill Sizes for A. L. A. M. Threads 62
Tap Drills for Machine Screw Taps 63
Twist Drill Dimensions for U. S. Thread Taps 64
Drills and Reamers for Dowel Pins 64
Double Depth of Threads 65
Tap Drills for Taps with "V" Thread 66
Drill End Lengths 67
TAPS
Tapping and Threading Speeds 68
Dimensions of Machine Screw Taps, Old Standard ... 69
Machine Screw Taps, Wells Bros. Co 70
Dimensions of Hand Taps 71
Dimensions of Tapper Taps 72
Dimensions of Briggs Standard Pipe Taps 73
Dimensions of Stove Bolt Taps 74
Dimensions of Taper Die Taps 75
Dimensions of Sellers Hobs 76
Dimensions of Square-Thread Taps 77
X CONTENTS
FILES
Page
Measurement of Files 78
Methods of Designating 78
Terms Used by Makers 78
Height of Work 78
Pickling Bath for Work to be Filed 78
Tooth Spacing 79
Teeth Per Inch 80
Shapes and Grades of Files 80-81
Maximum Efl&ciencies 82
' WORK BENCHES
Filing and Assembling Benches 84
Benches for Average Shop Work 84
Location of Benches 84
Modern Designs for Benches 85
High and Low Cost Benches 85
Material for Benches 85
Building Benches from Small Blocks 86
Height of Work Benches 86
Width and Thickness of Benches 86
SOLDERING
Cleaning the Joint 86
Strength of Soldered Joint 86
The Proper Heat for Soldering 86
Fluxes for Different Metals 86
Soldering Salts 86
Fluxes for Sheet Tin 86
Fluxes for Lead 86
Lead Burning 87
Fluxes for Brass ' 87
Fluxes for Copper 87
Fluxes for Zinc 87
Fluxes for Galvanized Iron 87
Fluxes for Wrought Iron or Steel 87
Making the Fluxes 88
Cleaning and Holding the Work . 89
Soldering with Tin Foil 89
Soldering Cast Iron 89
Cold Soldering Various Materials 90
Solders and Fusible Alloys 90
Composition and Melting Points of Solders and Fusible
Alloys 91
Hard Solders 91
Aluminum Solders 92
CONTENTS XI
GEARING
Page
Gear Teeth, Shapes of 93
Teeth and Parts 93
Table of Circular Pitch of Gears 94
Table of Diametral Pitch of Gears 95
Table of Corresponding Diametral and Circular Pitches. . 96
Chordal Pitch and Spur Gear Radius . 97
Table of Constants for Chordal Pitch 97
Table of Tooth Parts, Diametral Pitch : . . 98-99
Table of Tooth Parts, Circular Pitch loo-ioi
Diagram for Cast-Gear Teeth 102
Laying out Spur Gear Blanks . 103
Actual Sizes of Diametral Pitches 104-105
Laying Out Single Curve Teeth 106
Pressure Angles 106
La>dng Out Standard Teeth 107
Stub-tooth Gears 107
Fellows Stub-tooth Dimensions 108
Nuttall Stub-tooth Dimensions ^. . . . 108
Table for Turning and Cutting Gear Blanks .... 109-110
Table of Pitch Diameters of Standard Gears .... 111-114
Involute Gear Tooth Cutters 115
Table of Depth and Thickness of Teeth 115
Block Indexing in Cutting Gear Teeth 115
Table for Block Indexing 116
Metric Pitch, Formula and Table 117
Sprocket Wheels for Block Center Chains 118
Sprocket Wheels for Roller Chain 119
Bevel Gear Parts 120
Laying Out Bevel Gear Blanks 120
Proportions of Miter and Bevel Gears 121
Cutters for Bevel Gears 122
Table of Dimensions for Miter Gears 123
Bevel Gear Table and Examples of Use 124-125
Calculation of Spiral Gears, Table 126
Laying Out 45-deg. Spiral Gears 127
Figuring Spiral Gears 128-130
Real Pitches for Circular Pitch Spiral Gears 131
Table of Real Pitches for Circular Pitch Spiral Gears . 132-133
Spiral Gears, Formulas and Rules 134
Spiral Gear Table 13S
Chart of Spur Gear Cutters for Spiral Gears 136
Threads of Worms i37
Width of Face of Worm Wheels i37
Finding Pitch Diameter 138
Table of Worm Threads and Wheels , 139
xii CONTENTS /
MILLING AND MILLING CUTTERS
Page
Speeds and Feeds for Gear Cutting 140
Milling Machine Speeds and Feeds 141
Action of Milling Cutters 142
Form of Cutter Teeth 143
Power Required by Cutters . ., 144
Finish of Work 144
Chip Breaker 145
Taper Shank End Mills . 145
Spiral Shell Cutters . 146
Wide Spaced Tooth Cutters 147
Table of Pitches and Angles 148-151
Cam Milling
Milling Heart Shaped Cams 152
Method of Laying Out Cam 152
Selecting the Cutter 152
Locating Cam and Cutter at Start 152
Selecting the Correct Index Plate 152
Operating the Table for Successive Cuts on the Cam 153
Mining Cams by Gearing Up the Dividing Head .... 153
Diagram for Determining Angle of Index Head .... 153
Gearing the Machine for Cam Lobes of Different Leads 154
Method of Feeding the Work to the Cutter 154
Tables of Settings for Milling Screw Machine Cams 155-167
Indexing
Plain and Differential Indexing 168
General Principles of Differential Indexing 1 68-1 71
Tables of Dividing Head Gears for Indexing 172-189
Table for Indexing Angles 1 90-1 91
Milling Cutter Reamer and Tap Flutes
No. of Teeth in End Mills, Straight and Spiral Flutes . . 192
No. of Teeth in Inserted Tooth Cutters 192
Pitch of Metal Slitting Cutters 192
Pitch of Screw Slotting Cutters ■ . . . 192
No. of Teeth in Plain Milling Cutters 193
Form of Cutter for Milling Teeth in Plain Milling Cutters 193
No. of Teeth in Side or Straddle Mills 193
Angular Cutter for Milling Teeth in Side or Straddle Mills 193
No. of Teeth in Corner Rounding Concave and Convex
Cutters 194
Angular Cutter for Milling Teeth in Corner Rounding Con-
cave and Convex Cutters 194
No. of Teeth in Single and Double Angle and Spiral Mill
Cutters 194
CONTENTS xiii
Page
Cutter for Milling Teeth in Double Angle and Spiral Mill
Cutters ^ 194
No. of Flutes in Taps — Hand, Machine Screw, Tapper,
Nut and Screw Machine 19S
Tap Fluting Cutters 196
No. of Flutes in Taper and Straight Pipe Taps 196
Fluting Cutters for Taper and Straight Pipe Taps .... 196
No. of Flutes in Pipe Hobs, Sellers Hobs and Hob Taps . 196
Fluting Cutter for Hobs 196
No. of Flutes in Shell Reamers 197
Cutters for Fluting Reamers 197
No. of Flutes in Chucking and Taper Reamers 198
Diameter of Straddle Mills for Fluting Center Reamers 199
Cutter Key ways, Square and Half-Round 199
Table of Standard T-Slot Cutter Dimensions 200
Table of Largest Squares That Can Be Milled on Round
Stock 200
Table of Divisions Corresponding to Given Circumferential
Distances 201
Table for Milling Side Teeth in Milling Cutters 202
COLD SAWS
Cutting Speeds for Cold Saw Cutting-Off Machines . . . 203
Diagram of Saw Tooth 203
Table of Cutting Speeds 204
TURNING AND BORING
Table for Figuring Machine Time on Turned, Bored or
Faced Work 205
Formula for Machine Time on Turned, Bored or Faced
Work 206
Calculation of Rotary Cutting Speed 206
Efi&ciency Tool Tests 206
Cutting Lubricants for Various Materials 207
GRINDING AND LAPPING
Grinding Wheels and Grinding
Commercial Abrasives: Emery, Corundum, Carborundum,
and Alundum 208
Grit and Bond 208
Bonds of Abrasive Wheels 209
Grain and Grade 209
Table of Minimum Thickness of Elastic Wheels 210
Table of Minimum Thickness of Vitrified Wheels .... 210
Table of Minimum Thickness of Silicate Wheels 211
Grading of Wheels 211
xiv CONTENTS /
Page
Selection of Suitable Wheels . ' 212
The Combination Grit Wheel 212
Hard Wheels 212
Wheel Grades for Given Classes of Work 213
Speed and Efi&cient Cutting 213
Action of Wheels When Too Hard or Soft 213
When a Wheel Is Sharp 214
Contact of Wheels on Different Diameters, Flat Surfaces
and Internal Work 214
Selecting Wheels According to Contact 214
The Contact Area of a Wheel 215
Wheel Pressure and Wear 215
Wearing Effect of High Work Speeds 215
Grinding Allowance, Data 216
Grinding Hardened Work 216
Undercut Corners for Shoulders to be Ground 216
Grinding Allowances for Various Lengths and Diameters 217
Limit Gage Sizes for Finished Ground Work ....... 218
Use of Water 218
Use of Diamonds 218
Methods of Setting the Diamonds 219
Table of Grinding Wheel Speeds 220
Surface Speed of Wheels 221
Table of Circumferences for Surface Speeds and Revolu-,
tions 221
Grading Abrasive Wheels 222
Grade Marks and Lists of Standard Wheel Makers 222-223
Table of Grades of Wheels for Different Classes of Work 223
Shapes of Wheels 224-225
Mounting Grinding Wheels 226-227
General Suggestions for Operation 228
Magnetic Chucks 228
Hints on Use of Magnetic Chucks 229
Polishing Wheels 229
Care of Polishing Wheels 230
Speeds of Buffing Wheels 230
Lapping
Common Classes of Laps 231
Lapping Plate for Flat Work 231
Speed of Diamond Laps 231
Lapping Flat Surfaces 231
Lubricants in Lapping 232
Laps for Holes 232
Adjustable Laps 233
Advantages of Lead Laps 233
Various Types of Internal Laps 233
How to Do Good Lapping 233
Using Cast Iron, Copper and Lead Laps 233
CONTENTS XV
Page
Ring Gage and Other Work 234
A Lap for Plugs 234
Abrasives for Different Kinds of Laps 234
Diamond Powder in the Machine Shop 234
Grade of Diamond Used 234
Reduction Process 234
Setthng Diamond Powder in Oil 235
Table for Setding Diamond 235
Rolling the Diamond Powder into Laps 235
Diamond Laps 235
Tools Used in Charging Laps 235
Diamond Lap for Grinding Small Drills 235
Grinding Holes in Hard Spindles 236
Diamond Used on Boxwood Laps 236
Reamer and Cutter Grinding
Reamer Clearances ~ 237
Chucking Reamer Blade for Cast Iron and Bronze ... 237
Shape of Reamer Blade for Steel 237
Clearance of Reamer Blades 237
Grinding the Clearance on Various Classes of Reamers ." . 237
Table for Grinding Clearances on Different Sizes of
Reamers 238-239
Cup Wheel Clearance Table Giving Tooth Rest Settings
for Desired Clearance 240
Disk Wheel Clearance Table 240
OILSTONES AND THEIR USES
Data on Natural Stones 241
Data on Artificial Stones 241
Shapes and Sizes for Machine Shop Use 241-242
Shapes and Sizes for Mold and Die Work 243
Care of Oilstones 244
SCREW MACHINE TOOLS, SPEEDS AND FEEDS
Box Tools and Cutters 245
Roughing Box Tool with Tangent Cutter 245
Clearance for Box Tool Cutters 24,^
Sizes of Steel Recommended for Box Tool Cutters .... 246
Finishing Box Tool with Radial Cutter 246
Hollow Mills 246
Location of Cutting Edge and Rake for Hollow Mills . . 246
Hollow Mill Dimensions 247
Dies and Taps 247
Tapping Out Spring Dies 247
Spring Die Sizes 248
Sizing Work for Threading 248
xvi CONTENTS '
Page
Table of Over- and Under-size Allowances for Tapping
and Threading 249
Tap Lengths, Number of Flutes and Width of Lands . . 249
Forming Tool Diameters and Depths 250
Circular and Dovetail Forming Tools 251
Cutting Clearances on Forming Tools 251
Diameters of Circular Tools and Amount Usually Cut
Below Center 251
Finishing a Circular Tool to Correct Outline 252
Formulas for Obtaining Depths to Finish Circular Tool on
Center Line " 252
Dovetail Tool Depths 253
Finishing a Dovetail Forming Tool 253
Location of Master Tool in Finishing Circular and Dove-
tail Tools 253
Circular Tools for Conical Points 254
Finishing a Circular Tool to Produce a 60-deg. Cone 254
Finding Diameters of Circular Forming Tools 255
Table of Dimensions of Cutters for B. & S. Automatic
Screw Machines 256
Table for Finding Diameter of Circular Forming Tools for
B. & S.' Automatic Screw ]\Iachine 256-259
Hardening Spring Collets and Feed Chucks 260
Speeds and Feeds for Screw Machine Work
Table of Cutting Speeds and Feeds for Screw Stock . . . 261
Table of Cutting Speeds and Feeds for Brass 261
Table of Speeds and Feeds for Finish Box Tool 262
Table of Speeds and Feeds for Forming 263
Table of Speeds and Feeds for Drilling 264
Table of Speeds and Feeds for Reaming 265
Table of Speeds and Feeds for Threading 265
Rate of Feed for Counterboring 265
PUNCH PRESS TOOLS
Method of Finding the Diameter of Shell Blanks. .... 266
Diagrams and Formulas for Blank Diameters for Plain,
Flanged, Hemispherical and Taper Shells 267
Formulas and Table of Diameter of Shell Blanks. . . 268-269
Punch and Die Allowances for Accurate Work 270
Governing Size of Work by Punch and Die 270
Table of Clearances for Punch and Die for Different Thick-
ness and Material 271
Clearance for Punches and Dies for Boiler Work .... 271
Lubricants for Press Tools 272
Oiling Copper and German Silver Sheets for Punching . . 272
Mixture for Drawing Steel Shells 272
Preparations for Drawing Brass, Copper, etc 272
CONTENTS xvii
BROACHES AND BROACHING
Page
Application of Broaching 273
Shape and Spacing of Teeth for Square Holes 273
Broaching Round Holes 274
Saving Time in Broaching Out Square Holes ...... 275
Broaches for Automobile Transmission Gears 276
Diagram and Table for Standard Automobile 6-spline
Fittings 277
Diagram and Table for Standard Automobile lo-spline
Fittings 278
BOLTS, NUTS AND SCREWS
U. S. Standard Bolts and Nuts 279-281
Shearing and Tensile Strength of Bolts 279
Dimensions of U. S. Standard Rough Bolts and Nuts . . 280
Dimensions of U. S. Finished Bolts and Nuts 281
Sizes of Machine Bolts with Manufacturers' Standard
Heads . . 282
Diagrams of Set Screws 283
Set Screw Dimensions, Hartford Machine Screw Co.'s
Standard 283
Tables of Cap and Machine Screw Dimensions
Hexagon and Square Head Cap Screws 284
"Collar Head or Collar Screws 284
Fillister Head Cap Screws, P. & W. Standard 285
Flat, Round and Oval Fillister Head Cap Screws .... 286
Button Head Cap Screws 287
Flat and Oval Countersunk Head Cap Screws 287
Flat and Round Head Machine Screws, Amer. Screw Co.'s .
Standard 288
Fillister Head Machine Screws, Amer. Screw Co.'s Stand-
ard 289
Threads per Inch on Machine Screws, Amer. Screw Co.'s
Standard 290
A. S. M. E. Standard Form of Thread, Pitch Formula, etc. 290
Diagrams of Basic Maximum and Minimum Screw and
Tap Threads 291
Tables of A. S. M. E. Standard Machine Screw Dimensions
Outside, Root and Pitch Diameters of Standard Screws 292
Diameters of Taps for Standard Screws 293
Outside, Root and Pitch Diameters of Special Screws . . 294
Diameters of Taps for Special Screws 295
Dimensions of Oval Fillister Heads 296
Dimensions of Flat Fillister Heads 297
xviii CONTENTS
Page
Dimensions of Flat Countersunk Heads 298
Dimensions of Round or Button Heads 299
Nut and Bolt Tables
U. S. Standard Hot Pressed and Cold Punched Nuts . . , 300
Cold Punched Check and Jam Nuts 300
Manufacturers' Standard Hot Pressed and Forged Nuts . 301
Manufacturers' Standard Cold Punched Nuts 302
Manufacturers' Standard Narrow Gage Hot Pressed Nuts 303
Whitworth Standard Hexagonal Nuts and Bolt Heads . . 303
Bolt Heads
Button Head Machine, Loom and Carriage Bolts .... 304
Length of Bolts 304
Length of Threads Cut in Bolts 304
Round and Square Countersunk Head Bolts 305
Tap Bolts 305
Stove Bolts, Diameters and Threads 305
Automobile Bolt and Nut Standards Adopted by A. L.A.M. 306
Planer Nuts 307
CoupHng Bolts 307
Planer Head Bolts, Nuts and Washers 307
MISCELLANEOUS TABLES
Depths to Drill and Tap for Studs 308
Bolt Heads for Standard T-Slots 308
Eye Bolts 309
Spring Cotters 309
U. S. Standard Washers 310
Narrow Gage and Square Washers 310
Cast Iron Washers ■ 311
Riveting Washers 311
Machine and Wood Screw Gage Sizes 311
Coach and Lag Screws 312
Length of Threads on Coach and Lag Screws 312
Lag Screvv' Test 312
Wood Screws 313
Boiler and Tank Rivet Heads 314
Length of Round Head Rivets for Different Thicknesses
of Metal 315
CALIPERING AND FITTING
The Vernier and How to Read It 316
The Vernier Graduations 316
The Principle of the Vernier Scales 317
Reading the Micrometer 317
The Micrometer Parts 317
CONTENTS XIX
Page
The Ten-Thousandth Micrometer 318
Micrometer Graduations 318
Measuring Three-Fluted Tools with Micrometer and
V-block 318-319
Press and Running Fits
Parallel Press, Drive and Close Fits 319
Parallel Running Fits 319
Table of Limits for Press, Drive and Hand Fits 320
Table of Limits for Close, Free and Loose Running Fits . . 321
Shrink Fit Allowances 322
Limits in Shop Gages for Various Kinds of Fits . . . 322-323
Limits for Work Ground to Various Classes of Fits . 324-325
Limits in Plug Gages for Standard Holes 322
Allowances Over Standard for Force Fits 323
Allowances Over Standard for Driving Fits 323
Allowances Below Standard for Push or Keying Fits ... 323
Clearances of Running Fits 323
Metric Allowances for Fits of all Classes 325
Tables of Allowances (INIetric) for Various Classes of Fits 326
Press Fits for Wheel Hubs 327
Running Fits for Power Transmission Machinery .... 327
Making Allowances wdth the Calipers for Various Kinds
of Fits 328-331
Side Play of the Cahpers when Measuring for Running Fits 328
Table of Reduced Diameters Indicated by Side Play of
Calipers 328
Axial Inclination of CaUpers in Measuring for Shrink or
Press Fits 329
Table of Caliper Inclination for Allowances for Shrink or
Force Fits 329
Side Play of Calipers in Boring Holes Larger Than a Piece of
Known Diameter 330
Rule for Fiijding Variation in Size of Hole Corresponding to
Given Amount of Side Play 330
Allowing for Running and Driving Fits 331
Dimensions of Keys and Keyseats
Rules for Key and Key way Proportions 331
Key and Key way Dimensions 332
Dimensions of Straight Keys $S3
Square Feather Keys and Straight Key Sizes 334
Barth Keys 334
Pratt & Whitney Key System 335
Whitney lyeys and Cutters 336
Proportions of Key Heads 337
Table for Finding Total Keyway Depths 338-339
Table of Amount of Taper for Keys of Various Lengths 340
XX CONTENTS
TAPERS AND DOVETAILS
Measuring Tapers
Page
An Accurate Taper Gage . 341
Applications of the Taper Gage 342
Setting the Adjustable Gage Jaws by Means of Disks . . 342
Formulas for Use with Taper Gage _ . 343
Finding Center Distances between the Gage Disks .... 343
Finding the Disk Diameters 344
Finding the Amount of Taper per Foot 344
Finding the Width of Opening at the Ends of the Gage
Jaws 345
Diagrams and Tables of Standard Tapers
Brown & Sharpe Standard Tapers 346-347
Morse Standard Tapers 348-349
Morse Taper Short Shanks 350-351
Standard Tool Co.'s Standard Taper Shanks 352
Standard Tool Co.'s Short Taper Shanks 353
Reed Standard Tapers 354
Jarno Standard Tapers 354-355
Sellers Standard Tapers 356
Taper Pins and Reamers 357
Table of Drill Sizes for Taper Pins 358
Standard Taper Pins Used by the U. S, Ordnance De-
partment 359
Table Giving Total Amount of Taper for Work Tapering
from o to ij in. per foot and Ranging up to 24 in.
Long 360
Table of Tapers Per Foot in Inches and Corresponding
Angles 361
Table for Computing Tapers Corresponding to Any Given
Angle _ 362-363
Explanation of Table for Computing Tapers 364
Table for Dimensioning Dovetail Slides and Gibs . . 364-365
Measuring External and Internal Dovetails 366
Diagrams of Various Types of Dovetails 366
Table of Constants for Measuring Dovetails with Plugs . 367
Examples of Uses of the Table of Constants 367
Tool for Laying Out Angles Accurately 368
Table for Setting Tool for Laying Out Angles 368
Table of Gage Settings for Holes in a Circle 368
SHOP AND DRAWING ROOM STANDARDS
Standard Jig Parts
Drill Bushings 369
Dimensions of Fixed and Loose Bushings 369
CONTENTS XXI
Dimensions of Fixed Bushings for Tools Having Stop
Collars 370
Dimensions of Collar Head Jig Screws 370
Dimensions of Winged Jig Screws 370
Binding Screws 371
Supporting and Locking Screws 371
Dimensions of Nurled Head Jig Screws 372
Dimensions of Locking Jig Screws 372
Sizes of Straps for Jigs 372
Tables of Dimensions of Standard Machine Parts
Hand Wheels 373
Handles for Hand Wheels 374
Knobs 374
Ball Handles 375
Binder Handles 375
Single End Ball Handles 376
Ball Lever Handles . .• 376
Wing Nuts 377
Machine Handles 377
Thumb Nuts 378
Hook Bolts 378
Miscellaneous Tables
Standard Plug and Ring Gages 379
Counterbores with Inserted Pilots 380
Radial Bearings 381
Thrust Collar Bearings 382-383
Combined Radial and Thrust Bearings 384-385
Self-Aligning Radial Bearings 385
Integral Right-angle Triangles for Erecting Perpendiculars 386
Construction of Angles from Table of Chords 387
Chords of Arcs from 10 Minutes to 90 Degrees . . . 388-389
Table for Spacing Holes in Circles; Diameters i to 12,
Holes 3 to 32 390-391
Explanation of Table for Spacing Holes 392
Table of Sides, Angles and Sines for Spacing 3 to 500
Holes or Sides in a Circle 392-397
Lengths of Circular Arcs 398
Actual Cutting Speeds of Planers with Various Return
Ratios 399
Stock Allowed for Standard Upsets 399
Stock Required to Make Bolt Heads and Nuts, Mfrs'
Standard Sizes 400
Stock Required to Make Bolt Heads and Nuts, U. S.
Standard Sizes 401
Table of Board Feet in Pieces i to 24 in. Wide Up to 24
Feet Long . . „ - , 402
xxii CONTENTS
Page
Quick Way of Estimating Lumber for a Pattern 403
Table of Proportionate Weight of Castings to Weight of
Pattern 403
Degrees Obtained by Opening a Two-Foot Rule 403
Weight of Fillets 404
Table of Areas or Volumes of Fillets 404
MISCELLANEOUS INFORMATION
How to Lay Out a Square Corner 405
Speeds for Wood Turning 405
Cooling Hot Bearings 405
WIRE GAGES AND STOCK WEIGHTS
Twist Drill and Steel Wire Gage Sizes 406
Stubs' Gages 406
Different Standards for Wire Gages in the United States 407
Wire and Drill Sizes Arranged Consecutively .... 408-409
Stubs' Steel Wire Sizes and Weights 410
Music Wire Sizes 411
Weights of Sheet Steel and Iron, U. S. Standard Gage 411
Weights of Steel, Iron, Brass and Copper Plates, B. & S.
Gage 412
Weights of Steel, Iron, Brass and Copper Plates, B'ham
Gage . 413
Weights of Steel, Iron, Brass and Copper Wire, B. & S.
Gage - 414
Weights of Steel, Iron, Brass and Copper Wire, B'ham
Gage 415
Weights of Steel and Iron Bars per Linear Foot 416
Weights of Brass, Copper and Aluminum Bars per Linear
Foot 417
Weights of Flat Sizes of Steel 418
Weights of Seamless Brass and Copper Tubing 419
HORSE-POWER, BELTS AND SHAFTING
Explanation of Horse-Power 420
Steam Engine Horse-Power 420
Electrical Power 420
Gas Engine Horse-Power 420
Formula of A. L. A. M. Horse-Power Rating 421
Table of H. P. Ratings Based on A. L. A. M. Formula . . 421
Driving Power of Leather Belts 422
Factors for 180 deg. of Belt Contact 423
Factors for Varying Degrees of Belt Contact .• 423
Examples of Power Transmitted by Belts of Varying Sizes
and Speeds 424
Data on Pulleys and Ropes 424
CONTENTS xxui
Page
Horse-Power Transmitted by Manila Rope 425
Data of Manila Transmission Rope 425
Belt Fastenings • 426
Belt Hooks 426
Belt Lacings 426
Belt Studs 426
Lacing Belts with Leather 426
Lacing Belts with Wire 426
Strength of Lacings 427
Tension on Belts 427
AHgning Shafting by a Steel Wire 428-429
Table of Wire Sag for Lining Shafting 428-429
Table of Power Transmitted by Steel Shafting 430
Speeds of Pulleys and Gears 430
Rules for Finding Pulley and Geared Speeds 431
Tables of Circumferential Speeds 431-435
Power Required by Engine Lathes 436
Power Required by Axle Lathes 436
Power Required by Wheel Lathes 436
Power Required by Cylinder Lathes 436
Power Required by Vertical Boring Mills 436
Power Required by Horizontal Boring, Drilling and ]\iilling
Machines 436
Power Required by Cylinder Boring Machines 436
Power Required by Miscellaneous Machines 436
Power Required by Planers 436
Power Required by Frog and Switch Planers 436
Power Required by Plate Planers 436
Power Required by Rotary Planers 437
Power Required by Shapers 437
Power Required by Crank Slotters 437
Power Required by Plain Millers 437
Power Required by Universal Millers • 437
Power Required by Vertical Millers 437
Power Required by Vertical Slab Millers 437
Power Required by Horizontal Slab Millers 437
Power Required by Cylindrical Grinders 437
Power Required by Emery Grinders 437
Power Required by Miscellaneous Grinders 437
Power Required by Buffing Heads 437
Power Required by Vertical Drilling Machines 437
Power Required by Radial Drilling Machines 438
Power Required by Multiple Spindle Drilling Machines . 438
Power Required by Gear Cutters 438
Power Required by Cold Saws 438
Power Required by Bolt Cutters 438
Power Required by Bolt Pointers 438
Power Required by Nut Tappers 438
Power Required by Pipe Threading and Cutting-oif
Machines . 438
XXIV CONTENTS
Page
Power Required by Hammers 438
Power Required by Bulldozers, Forming or Bending
Machines • 438
Power Required by Bolt Headers and Upsetting Machines 438
Power Required by Hot Nut Machines 439
Power Required by Hydraulic Wheel Press 439
Power Required by Bending and Straightening Rolls . . . 439
Power Required by Notching Press 439
Power Required by Punches and Shears *. 439
Motors Usually Employed for Cranes and Hoists .... 439
Power Required for Planing Mill Equipment 440
Group Driving of Machines 441
Power Required for Punching 441
Power Required to Remove Metal 441
Factors in Power for Driving Machines 442
Data and Tables on H. P. to Drive Machines . . . 442-443
STEEL AND OTHER METALS
Heat Treatment of Steel 444
Molecular Changes in Cooling 444
Safe Temperatures for Steel 444
Methods of Heating 444
Furnaces for Different Fuels 444
Heating in Liquids 444
Baths for Heating 445
Gas as Fuel 445
Cooling the Steel 445
Baths for Cooling and Hardening 445
Annealing 446
Hardening Bath 446
Bath for Drawing Temper. 447
High Speed Steels > . 447
Casehardening 448
Harveyizing Process 448
Carbonization or Casehardening 448
Penetration of Carbon 448
Carbonizing Materials 449
Action of Wood Charcoal 449
Tests of Carbon Penetration 449-450
Effect of Composition on Strength 451
Effect of Hardening on Strength 451
Mechanical Properties When Annealed 451
Mechanical Properties When Hardened 451
Quenching Temperatures 452
Testing Pyrometers 452
Tests of Hardness 452
Brinell Test 452
Table of Brinell Hardness Numerals 453
Scleroscope Hardness Scale 454
CONTENTS XXV
Page
Fahrenheit and Centigrade Thermometer Scales 455
Conversion of One Thermometer to the Other 455
Alloys for Coinage 455
Composition of Bronzes 456
Bearing Metals 456
Bismuth Alloys, Fusible Metals 456
Alloys 457
Brass Alloys 457
Properties of IMetals 458
Shrinkage of Castings 458
Aluminum, Properties of 459
Aluminum, Melting, Polishing and Turning . 459
STEAM HAMMERS AND DROP FORGING
Capacity of Steam Hammers 460
Pressures for Steam Hammers 460
Boiler Capacity for Steam Hammers 460
Draft in Drop Forging Dies 461
Allowances for Shrinkage in Dies 461
Table of Draft Dimensions 462
Making Types 462
Mean Draft of Spherical End of Cyhndrical Type ' . . . 463
Finishing Semi-circular Impressions 463
Testing Accuracy of Semi-Circular Impressions 463
KNOTS, EYE-BOLTS, ROPES AND CHAINS
Knots and Slings for Handling Work 464-468
Table of Safe Loads for Eye-bolts 469
Table of Safe Loads on Ropes and Chains 469
GENERAL REFERENCE TABLES
Common Weights and Measures 470-471
Table of Weights of a Cubic Foot of Substance . . 471-473
Water Conversion Factors 473
Convenient Multipliers 474
The Metric System ' 474
Metric Weights and Measures 474-475
Metric and English Conversion Tables 475
Miscellaneous Conversion Factors 476
Decimal Equivalents of Fractions of Millimeters, Advan-
cing by i/ioo mm 476
Decimal Equivalents of Fractions of Millimeters, Advan-
cing by 1/50 and i mm 477
Equivalents of Inches in Millimeters 478
Decimal Equivalents of Fractions of an Inch,' Advancing
by 8ths, i6ths, 32ds, and 64ths 479
Decimal Equivalents of Fractions of an Inch, Advancing
by 64ths 479
;xxvi CONTENTS
Page
Decimal Equivalents of Fractions Below 1/2 in 480
Decimal Equivalents of Fractions Between 1/2 and i in. 481
Decimal Equivalent of Fractions and Nearest Equivalent
64ths 482-484
Table of Prime Number Fractions and Their Decimal
Equivalents 485
Equivalent of Inches in Decimals of a Foot 486-487
Squares of Numbers from o to 7 63/64 by 64ths . . . 488-489
Squares, Cubes, Square and Cube Roots of Fractions from
1/64 to I in 490-491
Squares, Cubes, Square and Cube Roots of Numbers from
I to 1000 492-501
Areas and Circumferences of Circles from i to 100 . . 502-507
Areas and Circumferences of Circles from 100 to 1000 508-513
Circumferences and Diameters of Circles 514
Reciprocals of Numbers from i to 1000 515-519
SHOP TRIGONOMETRY
Explanations of Terms • • • 520-521
Finding Depth of V-Thread 522
Finding Diagonal of Bar 522
Finding Square for Taps 522
Spacing Bolt Circles 523
Laying Out Jigs 523
Trigonometry Formulas 524
Use of Formulas 524
Table of Regular Polygons 525
Practical Examples 526
Finding Radius Without Center 526
Properties of Regular Figures: Circle, Triangle, Square,
Hexagon and Octagon 527-528
Table of Tangents and Co-tangents 529-540
Table of Sines and Co-sines 540-551
Table of Secants and Co-secants 552-563
DICTIONARY OF SHOP TERMS
Definitions and Illustrations of Shop Terms 564- -656
Index 657
THE AMERICAN MACHINISTS'
HANDBOOK
SCREW THREADS
CUTTING SCREW THREADS
Nearly all lathes are geared so that if gears ^having the same num-
ber of teeth are placed on both stud and lead screw, it will cut a thread
the same pitch as the lead screw. This is called being geared "even."
If the lathe will not do this, then find what thread will be cut with
even gears on both stud and lead screw and consider that as the pitch
of lead screw. In speaking of the pitch of lead screw it will mean
the thread that will be cut with even gears.
In cutting the same thread with even gears, both the work and the
lead screw are turning at the same rate. To cut a faster thread, the
lead screw must turn faster than the work, so the larger gear goes
on the stud and the smaller on the lead screw. To cut a slower
thread (finer-pitch or less lead), the larger gear goes on the screw
and the smaller on the stud.
Calling the lead screw 6 to the inch, what gears shall we use- to
cut an 8 thread?
Multiply both the lead screw and the thread to be cut by some
number (the same number for both) that will give two gears you have
in the set. If the gears vary by 4 teeth, try 4 and get 24 and 32 as
the gears. If by 5, you get 30 and 40 as the gears. Then as 8 is
slower than 6, the large gear goes on the lead screw and the small
one on the stud.
Cut an 18 thread with a 5-pitch lead screw and gears varying by
5 teeth. 5 X 5 = 25 and 5 X 18 = 90. There may not be a 90
gear, but you can use a 2 to i compound gear and use a 45 gear
instead. That is, put the 25 gear on the stud, use any 2 to i com-
bination between this and the 45 gear on the screw.
The 25 gear must drive the large gear of the 2 to i combination
and the small gear drive the 45-tooth gear, either directly or through
an intermediate.
In cutting fractional threads the same rule holds good. To cut
II J threads with gears that change by 4 teeth, use 4 X 6 = 54 and
4 X 11^ = 46, with the 24 gear on the stud and the 46 on the screw.
With gears changing by 5 this is not so easy, as 5 X 115- = 57i> an
impossible gear. Multiplying by 10 would give 60 and 115, not
much better. Multiply by 6 and get 6 X 6 = 36 and 6 X ni = 69,
neither of which is in the set. It seems as though 35 and 70 would
come pretty near it, but they will cut a 12 thread instead.
To find what thread any two gears will cut, multiply the pitch of
lead screw and the gear which goes on it and divide this by the gear
on the stud. Suppose we try 40 on the stud and 75 on the lead
I
SCREW THREADS
•a
u
I
u
u
O O
SH
GEARS FOR SCREW-CUTTING 5
screw. Multiply 75 by 6 = 450 and divide by 40 which gives ii^
as the thread that will be cut. Try 45 and 80. 6 X 80 = 480;
divided by 45 = lof, showing that the 40 and 75 are nearest and
• that to cut it exactly a special gear will have to be added to the set.
In reality the gears would not change by 5 teeth with a 6- pitch lead
screw.
Rules for screw cutting may be summed up as follows, always
remem.bering that the lead screw is the thread that will be cut
when gears having the same number of teeth are placed on both
screw and stud.
Having
A = True lead of screw
and
B = Thread to be cut
To Find
D
■■ Gear for stud
and
= Gear for screw
Rule
Multiply both A and B
by any one number
that will give gears
in the set. Put gear
A on stud and gear
B on lead screw.
A ■= True lead of screw-
B = Thread to be cut
C = Gear for stud
D = Gear for screw
Multiply B by J and
divide by A.
A = True lead of screw
B = Thread to be cut
D = Gear for screw
C = Gear for stud
Multiply A by D and
divide by B
A = True lead of screw
C = Gear for stud
D = Gear for screw
B = Thread that
will be cut
Multiply A by D and
divide by C
GEARS FOR SCREW-CUTTING
Gear trains for screw-cutting are usually arranged similarly to
the illustration, Fig. i. If the gear E on the lathe spindle has the saAe
number of teeth as the gear H on the stud S, the lathe is geared
even, i.e., gears having the same teeth placed on both stud and lead
screw will cut a thread like the lead screw. As shown, the gears
are out of mesh because the tumbler gears F and G do not mesh with
E; but moving the handle T down throws F into mesh with E so the
drive is through E, F, G, H, S and intermediate to L, driving it so
as to cut a right-hand screw if it is a right-hand thread, as is usually
the case. Raising handle / cuts out F entirely and reverses the direc-
tion of the lead screw.
4 SCREW THREADS
To follow the motion of a train of gears, take a stick (or your finger
if they are not running) and trace the motion from the driver to
the end as shown by the dotted lines in A, B, C and D.
When a lathe is compound geared the stud gear drives an auxil-
iary gear as A, which multiplies or reduces the motion as the case
may be. It will readily be seen, if the stud drives A and B drives L,
the motion will be exactly doubled because A has one-half the num-
ber of teeth in B,
A SCREW-THREAD ANGLE TABLE
The accompanying table gives the angle of helix of various pitches
and diameters with respect to a line perpendicular to the axis. These
angles were worked out with the idea of using them for grinding
thread tools for threads of various pitches upon different diameters
of work. This table will enable one to set the protractor at the
proper angle of side clearance for the work in hand and grind the
thread tool correctly without guesswork. This is based on the out-
side diameter. For coarse and multiple threads it is better to figure
on the pitch diameter.
Thread Angle Table
THREADS PER INCH = P
11
1
2
3
4
5
6
7
8
9
10
n
12
5*
i:
50°-54
32°-3i
22»-59
n°-^g
i4°-i8
""-59
io°-i9
9°-2
8°-3
7''-58
f-ii
6°- 1
40-23
23"- I
i5^-4«
I2°-l6
9°-39
8°- 8
7^-13
6"-37
5*^-23
:;"-2o
4"-40
4°-24
i"
32°-30
i7°-4i
ii^-,S«
9"- 3
7"- 1 6
b"-37
5-40
4"-33
4^- 3
4"- I
s"-37
S°- 3
1"
27^- 2
i4;;-i8
9°-38
7°-^ 5
5° -49
5^«
4°-io
3^-52
3^-15
3°-i3
2°-54
2°-26
f"
23°- 5
I2°- I
8°- 8
6^- 4
4^-52
4"- 3
3^-52
3"- 3
2°-43
2°-4I
2--10
2°- 2
i"
20^^- 4
I0°-20
7"^- I
5°-i2
4"-io
3^-28
2-59
2°-37
2--10
2-^-18
2"- 4
T°-SO
I "
i7"-30
^:- '
6^- 2
4^-33
3^-39
3"- 2
2^-36
2--17
2°- 2
2°-
i°-48
I°-n
i|"
iS"-40
8^- 4
.S^-23
4-- 4
3^-1^
2°-42
2"-I0
2"- 2
i"-48
i"-47
i"-37
T°-2T
!r
i4°-io
7^^-12
4^-48
3°-39
2-55
2°-26
2"- 2
i°-50
1^-44
i°-37
I°-27
T°-T3
i.t- 4
6^^7
4^-25
3^-10
2--40
2^-13
i"-54
i"-36
I°-29
I°-28
i°-iO
I°-6
ih"
11-59
6^- 4
4"- 3
3"- 3
2°-26
2°- 2
1-44
i°-3i
l'^-2I
l"-20
I"-I3
T°- T
if"
11^- 6
5^-36
3-44
2°-49
2°-i5
l"-^2
i"-36
l"-2I
i"-i5
i"-i4
i°- 7
56'
if"
IO°-26
s-^-ib
3^-20
2"-37
2"- s
i"-44
l"-20
i°-i8
I°-IO
i"- 8
I°- 2
53'
1 1"
q"-^o
4^-52
3"-!^
2"-26
i"-57
i°-37
I°-23
i"-i3
i°- 5
1°- 4
S8'
40'
2 *
0^- 4
4"- ^4
3 - 3
2°-l8
i^-So
i"-3i
i"-i8
i"- 8
i"- I
T°- 0
54'
4/
2}"
8"- 8
4"-0
2"-42
2"- 2
i"-37
l"-2I
i°- 8
i"- I
54'
w
49'
41'
2?"
C^-^
3°-39
2°-26
i°-49
1^-28
i°-i6
^°' ^
55'
49'
48'
43'
•^7^
2?"
b"-,n
3''-iQ
2°-i3
i°-40
I°-22
i"- 7
57'
so'
45'
44'
40'
3V
3 "
6^^- 4
3"- 3
2"- 2
i"-3i
i"-i3
i»- I
52'
46'
41'
40'
36'
3<^*
A SCREW-THREAD ANGLE TABLE 5
While the table is worked out for single threads, it can be used for
double or triple threads by considering the lead equal to the ad-
vance of the work in one revolution instead of — , as given in the
table. ^ P
It is customary in many shops to have several thread tools in stock
to cut these various thread angles, each cutting within a certain
range of angles. This table will be useful in determining the best
range for each thread tool.
P = Pitch = Threads per inch. — = Lead = L
C
D = Diameter of work in inches, tt = 3.1416 = —
C = Circumference of Work in inches — ir D
L Lead P t . f a 1
C = Circumference of Work ^ 7p = ^""^ent of Angle
Find Angle in Table of Tangents
Thread Angle Table
thee ads per inch = p
1%
13
14
15
16
18
20
22
24
26
28
30
32
w
i"
5°-36
f-^^
4''-5i
4°-33
4^-3
3'*-30
3''-iQ
3"- I
2''-45
2°-s6
2*^2.?
20-T7
-g"
,s"-45
3"-28
3^-14
3 - 3
2^-43
2°- 26
2°-I3
2"- I
I"- S3
i"-44
i°-37
T°-V
h"
2"-4Q
2^^-36
2^-26
2-^-17
2°- 2
i'^-49
1--40
I--SI
I°-24
i"-i8
I°-T^
T°- 8
i"
2"-I2
2"- 5
i"-57
1--48
1^^-37
l"-28
I°-20
i°-i3
i°- 8
i°- 3
59
54
'\>
i°-37
^^44
i°-30
i"-37
l''-24
i"-3i
i°-i8
I°-2I
I°-IO
i°- 3
i'^- 7
57'
I"- I
S3'
57
49
S3'
■ 45'
49'
42'
IS
I "
I°-24
1^-18
'!''3
i°- 8
l"- I
55
•^°,
45'
42
39'
36'
34'
ri"
i"-iS
i^-ii
I"- 5
i"- I
^<
49'
45^
40'
38
35'
32'
30'
^t
^^ 7
i°- 3
59
54'
49'
44,
40
37'
34
31
29'
27
li"
i°- I
57'
53'
50'
44'
40'
36'
33
31
28'
27'
25'
r¥
.0'
52'
49
46
40'
36'
33
30
28
26'
24'
2 V
It
52
48'
45'
42'
37
34;
3^!
28'
26
24'
23'
21'
48;
45'
42
40'
35
3^
28'
26'
24
22'
21'
19'
H"
45'
42'
39
37
33'
29'
27'
24'
23
21'
19'
18'
2 "
42;
40'
3b'
34'
31,
27'
25'
22'
21
19'
18'
1/
2t"
37
35'
32'
30'
27
24'
22
20'
19
18'
16'
15'
21"
34'
31'
29
27
24
22'
20'
18'
17
15'
14'
14'
2I"
3^!
28'
26'
25'
22'
20'
18'
17'
16
14'
iV
13'
3"
28'
26'
24'
23'
20'
18'
17'
IS'
14
13'
12'
ll'
SCREW THREADS
Figs. 2 and 3 show side and front elevations of the thread to(^
and of the protractor as applied to obtain the proper angle of side
clearance to cut a right-hand screw thread. The front edge of the
thread tool is used to determine the angle of side clearance. Fig. 4
shows a section taken along the line a b, Fig. 2. It will be noticed
that line e f is shorter than G H to give clearance to the cutting
edges of the thread tool, and also that G R is equal to H R and e S
is equal to / S. The angle of the hehx at half the depth of the
thread, Fig. 5, can be used, if desired, and can be approximated to
from the table, or figured exactly by the method given at the top of
the table.
TIG. 2
FIG. 3
FIG. 4 ^^^- 5
The Use of the Protractor
METRIC THREADS
Metric threads are measured in millimeter but are calculated by
the threads per centimeter. Any lathe with a pair of compound or
''translating gears" with 50 and 127 teeth, can cut metric threads,
the large gear being driven from the stud. Then the gears for the
number of threads per centimeter are figured the same as threads
per inch as on page 3.
MULTIPLE THREAD CUTTING
^ The accompan}dng table will be found useful when cutting mul-
tiple threads. When one thread is cut, the feed nut may be opened
(the spindle of course being stopped) and the carriage moved along
by hand the distance given in the table; the nut is then closed on
the screw and the next thread cut. This is a quick and sure method
of starting the second, third or fourth thread where the lead screw
of the lathe is of the pitch given in the table.
MULTIPLE THREAD CUTTING
Table for Multiple Thread Cutting
Cut
Thread on Lead
Screw-
Move Carriage
DOUBLE
I
Even
J inch
li
Any
2 inch
li
Any
I inch
2
4
J inch
2i
Any
2 inch
2h
An}^
I inch
3
Even
J inch
3i
Any
'
2 inch
3^
Any
I inch
4
8
i inch
4i
Any
2 inch
4^
Any
I inch
5
Even
^ inch
5i
Any
I inch
TRIPLE
I
6
iv
or
2 threads on
lead screw
li
6
I^
or
8 threads on
lead screw
I^
6
2/y
or
4 threads on
lead screw
2
6
1^
or
I thread on lead screw
2i
6
li''
or
8 threads on
lead screw
2h
6
f'
or
4 threads on
lead screw
QUADRUPLE
I
4
iinch
a
Any
I inch
li
Even
J inch
2
8
I inch
2i
Any
I inch
2i
Even
^ inch
To cut a double thread screw 3I to the inch: the lathe must be
geared the same as for a single, triple or quadruple thread. The
tool will of course have to be the same width and the depth of cut
the same as for a 7 per inch screw. After the first thread is cut it
will appear very shallow and wide. With the lathe spindle idle,
the nut is opened and the carriage moved (in either direction) i
inch; the nut is then closed on the lead screw and the tool is in the
proper position to make the second cut.
If the carriage were moved 2 inches, the tool could follow exactly
the first groove cut. In the case of a triple-thread screw, if the car-
riage were moved 3 inches, the tool would follow its original path,
and it would do the same in the case of a quadruple thread if moved
4 inches.
8
SCREW THREADS
The carriage can, of course, be moved i inch and the nut closed
no matter what the pitch of the lead screw may be (unless it is frac-
tional), but in order to close the nut after moving J inch, the screw
must have some even number of threads per inch.
As will be seen by referring to the table, a lead screw with any
even number of threads per inch is used in a number of cases, while
in several other instances the screw may be of any pitch — either
odd or even. In certain cases 4 and 8 per inch lead screws are
specified; and in cutting triple threads a 6 per inch screw is required.
Fig. 6. — Face-Plate for Multiple Thread Cutting
FACE-PLATE FOR MULTIPLE THREAD CUTTING
Fig. 6 shows a face-plate fixture used on various numbers of
threads. On an ordinary driving plate is fitted a plate having, as
shown, twelve holes enabling one to get two, three, four or six leads
if required. This ring carries the driving stud, and is clamped at
the back of the plate by two bolts as an extra safeguard. All that
is necessary in operation is to slack off the bolts, withdraw the index
pin, move the plate the number of holes required, and re-tighten
the bolts. It is used on different lathes, as occasion requires, by
making the driving plates alike and drilling a hole for the index pin.
It is found that the index pin works best when made taper, and a
light tap is sufficient to loosen or fix it.
CUTTING DIAMETRAL PITCH WORMS IN THE LATHE
The .accompanying table is to be used in cases where fractional
worm- thread cutting is necessary for diametrical pitch worm threads
to mesh into diametral-pitch worm gears.
CUTTING DIAMETRAL PITCH WORMS 9
Table of Change Gears for Diametral Pitch Worms
t^^A ^i
At*-
1^
0^
Pitch of Lead Screw
2
3
4
5
6
7
8
10
2 I
078"
.487"
.526;'
¥
¥
¥
¥-
¥
¥
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iffi
2i
862"
•390"
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If
W
W
¥
W-
¥
¥b^
W
3
719"
•?25"
•3 so,,
1!
¥
1!
W
¥
¥
¥1^
W
3i
616"
.278"
.300'/
If
W
W
^i
¥^
¥
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4
540"
• 243*
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431"
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.210"
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270"
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180"
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.048"
.053"
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m
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Formula:
22 X Lead Screw
7 X Diametral Pitch
= Ratio of Wheels.
355 to 113 is more accurate but requires odd gears; a 71 tooth
gear and a 5 to i compound gives 355.
In the first column is found the diametral pitch to be cut. In the
second column is found the corresponding single depth of the worm
thread. Under the third column is found the width of the tool at
the point, the tool being the regular 2g-degree included angle. In
the fourth column is found the width at the top of the worm thread.
The next heading in the chart is " Pitch of lead screw," and here
are found different pitches of lead <icrews from 2 to 10.
10 SCREW THREADS
Example: Suppose it is desired to cut a worm thread of 4 diametral
pitch on a single-geared lathe having a 6-pitch lead screw. Now,
opposite 4 in the first column find the single depth of worm thread,
or 0.540 inch; and continuing in the same direction from left to
right, under the next column find the width of the worm-thread tool
at the point or end, which is 0.243 inch, and so on to the next column
where is found the width of the worm thread at the top, which is
0.263 inch. Say there is a 6-pitch lead screw on the lathe. Then
follow right-on in the same direction until coming to the square
under 6, and the gear, will be in the ratio of ^j. Of course there is
no 7 gear on the lathe, so simply bring the fraction ^ to higher
denominations, say, V X f = If: that is, put the 99 gear on the
spindle or stud, and the 21 gear on the screw. Then use a gear of
any convenient size to act as an intermediate gear, and thus connect
the gear on the spindle with the gear on the screw. Taking the
fraction ^ and multiplying the numerator and denominator by 4,
would give VV ^s the two gears to be used. It will be seen that this
last fraction simply changes the number of teeth in the gears, but
does not change the value of the fraction; thus there is the same ratio
of gears.
Take another case: Suppose it is desired to cut a 20-diametraI
pitch worm thread in a lathe having a 4-pitch lead screw. What
would be the necessary gears to cut the desired thread? Next to
20 in the first column is found the single depth of the worm thread,
which is 0.108 inch. Continuing on, reading from left to right as
in the first case, and 0.048 inch is found as the width of the tool at
the point. In the next column is found the width at the top of the
worm thread, which in this case is 0.053 inch. Under column 4, and
opposite 20, are found the gears necessary for cutting a 20-diametral
pitch worm thread in a lathe with a 4-pitch lead screw. The gears
2 2 stud
thus found, nameh', — may not be in the regular set of gears
•"35 screw
furnished with the lathe. In that case double up on both and make
it — ^ , which is the same in value. The two examples thus
70 screw
worked out could have been cut on lathes with lead screws having
any number of threads per inch, with the same result. One point
in cutting these threads is that the tool must be of exact dimensions
all over, for if it is not exactly 29 degrees included angle, or the point
is not as it should be for width, then there will be an error in the
worm thread all around.
THE BROWN & SHARPS 29-DEGREE WORM THREAD
AND THE ACME 29-DEGREE STANDARD
SCREW THREAD
There seems to be some confusion among mechanics regarding
the 29-degree Acme standard screw thread and the Brown & Sharpe
29-degree worm thread.
The sketches, Figs. 7 and 8, show plainly the diflference be-
tween threads of the same pitch in the two systems. The sectional
MEASUREMENT OF V-TOOLS
II
views are of threads of one-inch linear pitch drawn to scale to the
proportions given by the thread formulas in connection with the
complete tables of the two systems of threads as given on pages fol-
lowing. The clearance for bottom of thread is the same, o.oio inch,
for all pitches. See formula on page 24 for correct dimensions.
h .6345'-^ ^3655^
Fig. 7 ^Acme 29-Degree Screw Thread
Fig. 8. — Brown & Sharpe 29-Degree Worm Thread
The worm thread is based on the linear pitch of the worm and
proportions figured same as rack tooth with varying clearances in
bottom. B. & S. 29-deg. screw thread has a uniform clearance of
0.005 inch for all pitches. Do not confuse the two threads.
MEASUREMENT OF V-TOOLS
The accompanjdng table of angle measurements should prove of
convenience to all who make tools for cutting angles or make the
gages for these tools.
The principle here adopted is that, on account of the difl&culty
and in some cases the impossibility of measuring the tool at its point,
the measurement is taken on the angle of the tool at a given distance
from the point. In this case the true measurement will be less than
the actual measurement by an amount equal to twice the tangent of
half of the angle multiplied by the distance of the line of measure-
ment from the point. ,
12
SCREW THREADS
For making the measurement the Brown & Sharpe gear-tooth
caliper may be used. Fig. 9 shows this tool in position for measur-
ing. The depth vernier A is set to a given depth h, and the meas-
urement is taken by means of the vernier B. The width of the tool
point X is equal to the measurement on the line a b less 2hl tan. — ) . To
use the table, h is always taken to be xV i^ch, which is found to be
a convenient depth for most work. If a greater depth is required,
all that is necessary is to multiply the figures given by the ratio of
the required depth to j^ inch. For instance, if the depth is required
KK
!^/6 P-1
Fig. 9. — Measuring Thread Tools
to be I inch, the figures given are multiplied by 2. In the great
majority of cases, jq ^'^^^ be found a suitable value for //, when to
find the width of the point x it is merely necessary to deduct the
, C
tan. —
2
value of — - — for the angle required, which can be obtained at a
8
glance from the table.
In the case of the Sellers or United States standard thread, the point
of the tool should be one-eighth of the pitch of the screw, while in
the Whitworth standard, as shown, the point of the tool would be
one-sixth of the pitch if it were not rounded. By using these fig-
ures in combination with the table, it can be determined when suffi-
cient has been ground from the point of the tool.
The table is called "Table for Angle Measurements," because if
a sharp angle, that is, one without the point ground away, is meas-
ured as above, this measurement, by reference to the table, will give
the angle direct.
GRINDING THE FLAT ON THREAD TOOLS 13
Table for V-Tool Angle Measurements
c
c
c
/<i>z. —
tan. —
tan. -
Degrees
2
Degrees
2
Degrees
2
8
8
8
I
O.OOII
31
0.0346
61 *
0.0736
2
0.0022
32
0.0358
62
0.0751
3
0.0033
33
0.0370
63
0.0766
4
0.0044
34
0.0382
64
0.0781
0.0055
35
0.0394
65
0.0796
6
0.0066
36
0.0406
66
0.081 1
7
0.0077
37
0.0418
67
0.0827
8
0.0088
38
0.0430
68
0.0843
9
0.0099
39
0.0442
69
0.0859
10
O.OIIO
40
0.0454
70
0.0875
II
O.OI2I
41
0.0466
71
0.0891
12
0.0132
42
0.0489
72
0.0908
13 •
0.0143
43
0.0492
73
0.0925
14
0.0154
44
0.0505
74
0.0942
15
0.0165
45
0.0518
75
0.0959
16
0.0176
46
0.0531
76
0.0976
17
0.0187
47
0.0544
77
0.0994
18
0.0198
48
0.0557
78
O.IOI2
19
0.0209
49
0.0570
79
0.1030
20
0.0220
50
0.0583
80
0.1048
21
0.0231
51
0.0596
81
0.1067
22
0.0242
52
0.0609
82
0.1086
23
0.0253
53
0.0623
83
O.IIO5
24
0.0264
54
0.0637
84
O.II25
25
0.0275
55
0.0651
85
O.II45
26
0.0286
56
0.0665
86
O.I165
27
0.0298
57
0.0679
87
O.I186
28
0.0310
58
0.0693
88
0.1207'
29
0.0322
59
0.0707
89
0.1228
30
0.0334
60
0.0721
. 90
0.1250
GRINDING THE FLAT ON THREAD TOOLS
To facilitate grinding the correct width of flat for the single-point
inserted tool to cut United States standard form of threads the ac-
companying table on pages 14 and 15 has been prepared. The dis-
tance from the point of the tool to the back is first measured with
the micrometer, then the point of the tool may be ground off until
the micrometer measurement from the back is equal to the whole
depth minus dimension Ay when we may be sure, without under-
taking the difficult job of measuring it directly, that the flat B has
the proper width. The dimensions A and B for pitches from i to
64 threads per inch are included in the table.
X4
SCREW THREADS
Table for Grinding Flat End of Tool for Cutting U. S.
Form of Thread
..J.
Threads
per Inch
Pitch
A
B
C
Double
Depth
Depth
I
1. 000
.1064
.125
.1082
1.299
.6495
2
.5000
.0532
.0625
.0541
.6495
••3247
3
'3333
•0355
.0416
.0360
•433
•2165
4
.2500
.0266
.0312
.0270
.3247
.1623
5
.2000
.0213
.0250
.0216
.2598
.1299
6
.1666
.0177
.0208
.0180
.2165
.1082
7
,1428
.0152
.0178
.0154
•1855
.0927
8
.1250
•0133
.0156
•0135
.1623
.0812
9
• nil
.0118
.0138
.0120
•1443
.0721
lO
.1000
.0106
.0125
.0108
.1299
.0649
II
.0909
.00963
.0113
.0098
.1180
.0592
12
.0833
.00S86
.0104
.0090
.1082
.0541
13
.0769
.00818
.0096
.0083
.0999
.0499
14
.0714
.00758
.0089
.0077
.0920
.0460
15
.0666
.00707
.0083
.0071
.0866
.0433
i6
.0625
.00673
.0079
.0068
.08 T 2
.0406
17
.0588
.00620
•0073
.0063
.0764
.0382
i8
.0555
.005S8
.0069
•0059
.0721
•0360
19
.0526
.00554
.0065
.0056
.0683
.0341
20
.0500
.00530
.0062
.0054
.0649
.0324
21
.0476
.00503
.0059
.0051
.0618
.0309
22
.0454
.0048
.0056
.0049
.0590
.0295
23
.0431
.00451
•0053
.0046
.0564
.0282
24
.0416
•00433
.0052
.0045
.0541
.0270
25
.0400
.00426
.0050
•0043
.0519
.0259
26
.0384
.00409
.0048
.0041
.0491
•0245
27
.0370
•00393
.0046
.0040
.0481
.0240
28
.0357
•00375
.0044
.0038
.0463
.0231
29
•0344
.00366
•0043
•0037
.0447
.0223
30
•0333
.00354
.0041
.0036
•0433
.0216
31
.0322
•00341
.0040
•0035
.0419
.0209
32
.0312
.00332
•0039
.0034
•0405
.0202
GRINDING THE FLAT ON THREAD TOOLS
15
Table for Grinding Flat End of Tool for Cutting U. S.
Form of Thread
Threads
per Inch
Pitch
A
B
C
Double
Depth
Depth
33
.0303
.00315
.0037
.0032
.0393
.0196
■34
.0294
•00307
.0036
.0031
.0382
.0191
35
.0285
.00295
•0035
.0030
.0370
.0185
36
.0277
.00289
.0034
.00295
.0360
.0180
37
.0270
.00281
•0033
.00286
.0350 •
•0175
38
.0263
.00272
.00325
.00282
.0341
.0170
39
.0256
.00268
.00320
.00277
.0333
.0166
40
.0250
.00264
.00312
.00270
.0324
.0162
41
.0243
.00255
.00303
.00262
.0319
•0159
42
.0238
.00251
.00295
.00257
.0309
•01545
43
.0232
.00247
.00290
.00251
.0302
.01520
44
.0227
.00238
.00283
.00245
.0295
.0147
45
.0222
.00233
.00277
.00240
.0290
.0145
46
.0217
.00230
.00271
.00235
.0282
.0141
47
.0212
.00225
.00265
.00230
.0274
•0137
48
.020S
.00221
.00260
.00225
.0270
.0135
49
.0204
.00217
.00255
.00220
.0263
.0131
50
.0200
.00213
.00250
.00216
.0258
.0129
51
.0196
.00208
.00245
.00212
.0254
.0127
52
.0192
.00204
.00240
.00208
.0249
.01245
53
.0188
.00200
.00235
.00203
.0245
.01225
54
.0185
.00196
.00231
.00200
.02405
.01202
55
.0181
.00192
.00226
.00196
.0236
.0118
56
.0178
.00189
.00222
.00192
.0232
.0116
57
•0175
.00185
.00218
.00189
.0228
.0114
58
.0172
.00184
.00215
.00186
.0223
.01115
59
.0169
.00180
.00211
.00183
.02201
.0110
60
.0166
.00177
.00208
.00180
.02165
.01082
61
.0163
.00173
.00203
.00177
.02119
.01059
62
.0161
.00172
.00202
.00175
.02095
.01047
63
.0158
.00169
.00198
.00171
.02061
.01030
64
.0156
.00167
.00196
.00169
.02029
.01014
l6 SCREW THREADS
Table of U. S. Standard Screw Threads
-P a
[p = Pitch =
Ho. Threads per Inch
Formula I d= Depth = p x .64952
f = riat=-E.
Diam.
Threads
Pitch
Depth of
Diam. at Root
Width of
of Screw
to Inch
Thread
of Thread
Flat
i
20
.0500
•032^
.185
.0063
T%
l8
•0556
.0361
.2403
.0069
1
i6
.0625.
'^405
.2936
.0078
T?
14
.0714
.0464
•3447
.0089 '
i
13
.0769
.0499
.4001
.0096
A
12
•0833
.0541
.4542
.0104
t
II
.0909
.0591
.5069
.0114
f
lO
.1000
.0649
.6201
.0125
1
9
.ilil
.0721
•7307
•0139
8
.1250
.0812
.8376
.0156
i|
7
.1429
.0928
•9394
.0179
li
7
.1429
.0928
1.0644
•0179
If
6
.1667
.1082
1-1585
.0208
i^
6
.1667
.1082
1-2835
.0208
If
5^
.1818
.1181
1.3888
.0227
5
.2000
.1299
1.4902
.0250
Is
5
.2000
.1299
1. 6152'
.0250
2
4\
.2222
.1444
i^7ii3
.0278
2i
Ah
.2222
.1444
1.9613
.0278
2h
4
.2500
.1624
2.1752
•0313
2\
4
.2500
.1624
2.4252
-0313
3
3i
.2857
.1856
2.6288
-0357
3i
3h
.2857
.1856
2.8788
•0357
3^
3i
•3077
.1998
3-1003
-0385
3l
3
•^^iZ
.2165
3-3170
.0417
4
3
•3333
.2165
3-5670
.0417
4i
2i
.3478
•2259
3.7982
•0435
4^
2l
.3636
•2362
4.0276
•0455
4f
2f
.3810
•2474
4.2551
.0476
5
2^
.4000
.2598
4.4804
.0500
5i
2^
.4000
.2598
4-7304
.0500
5^
2|
.4210
•2735
4-9530
.0526
5i
2|
.4210
•2735
5.2030
.0526
6
2i
•4444
.2882
5-4226
•0556
SHARP V THREADS
17
Table of Sharp "V" Screw Threads
p = Pitch = \
Formula ^ No. Threads per Inch
d = Depth = p X .86603
Diam.
No. Threads
Pitch ?
epth of
Diam. at Root
of Screw
per Inch
""liread
of Thread
I
20
.0500
0433
.1634
A
18
•0556
0481
.2163
1
16
.0625
0541
.2667
tV
14
.0714
0618
.3140
h
12
•0833
0722
•3557
t\
12
•0833
0722
.4182
t
II
.0909
0787
.4676
H
II
.0909
0787
•5301
f
10
.1000
0866
.5768
if
10
.1000
0866
•6393
i
9
.iiii
0962
.6826
11
9
.iiii
0962
•7451
• I
8
.1250
1083
.7835
li
7
.1429
1237
.8776
li
7
.1429
1237
1.0026
If
6
.1667
1443
1.0864
i^
6
.1667
1443
1.2114
If
5
.2000
1733
1.2784
If
5
.2000
1733
1.4034
i|
4h
.2222
1924
1.4902
2
4h
.2222
1924
1. 6152
2i
4h
.2222
1924
1.7402
2}
4h
.2222
1924
1.8652
2f
4h
.2222
1924
1.9902
2^
4
.2500
2165
2.0670
2f
4
.2500
2165 .
2.1920
2|
4
.2500
2165
2.3170
2|
4
.2500
2165
2.4420
3
3h
•2857
2474
2.5052
3i
3i
.2857
2474
2.6301
3i
3h
.2857
2474
27551
3l
3i
•3077
2666
2.8418
3^
3i
•3077
2666
2.9668 ■
3f
3i
•3077
2666
3.0918
3f
3
'3333
.2886
3.1727
3l
3
■3333
.2886
32977
4
3
■3333
.2886
3.4227
l8 SCREW THREADS
Table of Whitworth Standard Screw Threads
fp = Pitch =-
I No^ Threads pei Inch
Formula ^ d = Depth = p x .64033
( r=Eadius=p x .1373
Diam. of Screw
No. of
Threads
per inch
Pitch
Depth of
Thread
Diam. at Root
of Thread
i
20
.0500
.0320
.i860
A
l8
•0556
•0356
.2414
t
i6
.0625
.0400
.2950
tV
14
.0714
•0457
.3460
^
12
•0833
•0534
•3933
t\
12
•0833
•0534
•4558
f
II
.0909
.0582
.5086
H
II
.0909
.0582
•57"
f .
lO
.1000
.0640
.6219
if
lO
.1000
.0640
.6844
i
9
.IIII
.0711
•7327
I
8
.1250
.0800
•8399
li
7
.1429
.0915
.9420
li
7
.1429
.0915
1.0670
if
6
.1667
.1067
1.1616
i^
6
.1667
.1067
1.2866
if
5
.2000
.1281
1.3689
If
5
.2000
.1281
1-4939
2
4^
.2222
.1423
1-7154
2i
4
.2500
.1601
1.9298
2|
4
.2500
.1601
2.1798
2|
3i
.2857
.1830
2.3841
3
3i
.2857
.1830
2.6341
3i
3i
•3077
.1970
2.8560
3i
3i
•3077
.1970
3.1060
3i
3
'3333
.2134
3-3231
4
3
'3333
•2134
3-5731
4i
2|
.3478
.2227
4.0546
5
2f
•3636
.2328
4.5343
5i
2f
.3810
.2439
5.0121
6
2^
.4000
.2561
5-4877
BRITISH ASSOCIATION THREADS
Table of British Association Screw Threads
19
rp = Pitch
Formula < d^ Depth = p x !6
2 X p
r = Radius =-
U
Diam.
of Screw
Approxi-
I
Depth
Diam.
Num-
mate F
itch
Approximate
of
at Root of
ber
Diam. n
am.
Pitch Inches 1
hread
Thread
mm.
Inches
mm.
inm.
0
6.0
.236 I
0
•0394
6
4^8
I
5-3
.209
9
•0354
54
4.22
2
4-7
.185
81
.0319
485
3^73
3
4.1
.161
73
.0287
44
3.22
4
3-6
.142
66
.0260
395
2.81
5
3-2
.126
59
.0232
355
2.49
6
2.8
.110
53
.0209
32
2.16
7
2-5
.098
48
.0189
29
1.92
8
2.2
.087
43
^0169
26
1.68
9
1.9
•075
39
•0154
235
1-43
10
1-7
.067
35
.0138
21
1.28
II
1-5
•059
31
.0122
185
I -13
12
1-3
.051
28
.0110
17
.96
13
1.2
.047
25
.0098
15
•9
14
I.O
•039
23
.0091
14
.72
15
•9
•035
21
.0083
125
.65
16
•79
.051
19
.0075
115
•56
17
.70
.028
17
.0067
10
•50
18
.62
.024
15
.0059
09
•44
19
•54
.021
14
•0055
085
•37
20
.48
.019
12
.0047
07
•34
21
.42
.017
II
.0043
065
.29
22
•37
.015
10
.0039
06
.2.';
23
■33
.013
09
•0035
055
.22
24
.29
.oil
08
.0031
05
.19
25
•25
.010
07
.0028
04
•17
20 FRENCH (METRIC) STANDARD SCREW THREADS
i~^'i^ — J 1^?= Pitch
{p= Pitch /
d = Depth = p X .6495
f=Elat = P-
Q
Diameter of
Pitch
Diameter at Root
Width of
Screw mm.
mm.
of Thread mm.
Flat mm.
3
0-5
2-35
.06
4
0.75
3-03
.09
5
0-75
4.03
.09
6
I.O
4.70
.13
7 ^
I.O
5-70
.13
8
1.0
6.70
•13
8
1.25
6.38
.16
9
I.O
7.70
•13
9
1.25
7.38
.16
lO
1-5
8.05
.19
II
1-5
9-05
.19
12
1. 5
10.05
.19
12
1-75
9-73
.22
14
2.0
11.40
.25
i6
2.0
13.40
•25
i8
2.5
14-75
.31
20
2-5
16.75
.31
22
2-5
18.75
•31
22
3'0
18.10
•38
24
3-0
20.10
.38
26
3-0
22.10
-38
27
3'0
23.10
.38
28
3-o"
24.10
.38
30 ■
3-5
2545
•44
32
3-5
2745
44
33
3-5
28.45
44
34
3-5
2945
.44
36
4.0
30.80
•5
. 38
4.0
32.80
.5
39
4.0
33-80
.5
40
4.0
34.80
.5
42
4.5
36.15
.56
44
4-5
38.15
.56
45
4-5
39.15
.56
46
4.5
40.15
.56
48
5-0
41.51
. -63
50
5-0
43.51
.63
52
5-0
45-51
'63
56
5-5
48.86
.69
60
5-5
52.86
.69
64
6.0
56.21
.75
68
6.0
60.21
.75
72
6.5
63.56
.81
76
6.5
67.56
.81
80
7.0
70.91
.88
INTERNATIONAL STANDARD THREADS
21
Table of International Standard Screw Threads
dimensions in millimeters
Formula
rp = Pitch
<|d = Depth= p
U
X .64952
f =FIat
Diam.
Diam.
Diam.
Diam.
of
Pitch
of
Pitch
of
Pitch
of
Pitch
Screw
Screw
Screw
Screw
6
I.OO
18
2.50
39
4.00
68
6.00
7
I.OO
20
2.50
42
4-50
72
6.50
8
1-25
22
2.50
45
4-5°
76
6.50
9
1.25
24
3.00
48
5.00
80
7.00
lO
1.50
27
3.00
52
5.00
88
7-50
II
1.50
30
3-5°
56
5-5°
96
8.00
12
1-75
33
3-50
60
6.00
116
9.00
14
2.00
36
4.00
64
136
10,00
i6
2.00
The "International Standard" is the same, with modifications
noted, as that now in general use in France.
INTERNATIONAL STANDARD THREADS
At the "Congress International pour L'Unification des Filetages,"
held in Zurich, October 24, 1898, the following resolutions were
adopted :
The Congress has undertaken the task of unifying the threads of
machine screws. It recommends to all those who wish to adopt the
metric system of threads to make use of the proposed system. This
system is the one which has been established by the " Society for the
Encouragement of National Industries," with the following modi-
fication adopted by this Congress.
I. The clearance at the bottom of thread shall not exceed -^ part
of the hight of the original triangle. The shape of the bottom of
the thread resulting from said clearance is left to the judgment of
the manufacturers. However, the Congress recommends rounded
profile for said bottom.
3. The table for Standard Diameters accepted is the one which
has been proposed by the Swiss Committee of Action, (This table
is given above.) It is to be noticed especially that 1.25 mm. pitch
is adopted for 8 mm. diameter, and 1.75 mm. pitch for 12 mni.
diameter. The pitches of sizes between standard diameters indi-
cated in the table are to be the same as for the next smaller standard
diameter.
22
SCREW THREADS
/
in roOO t^OO O f^ w ^oo ■^ N ^ M moo O lo N O^O H vo ^ fO O Ov O
<N ro fO 3- 10\0 t^ Ov O M ro "TO OO M •^OC MOO rfl-i 0>10000 f ^ t^
OOOOOOOOwHMHMMNOiNrOrO'TlO 10\0 t^ t>-QO 0> 0
dddddddddddddddddddddddo'oddd
VO 00 0> c^ Tj- t^ Oi fOO O "^OO CSvO ^cOw O t^-^tMOO JAOvOrOrOt^
OdOwwMHNMcoro^O'*^ lO'O t^oo d\ M CO ■^^ r^ dv M CO •*
HMHI-ltHMMON
cjMiot^ ^^u-!C^•*r^O^^C^'*0^'tOlO' O'OO 00 00 oo 00 t^ r^ t^
Mt-iM»«HOioicNC)orofOfO*^^io too O r^co 0\0 M cocoioior^
qqqoooqooooooooooooooooooqqq
dddddddddddddddddddddddddddd
."2^
^
O 00 fOO O (^ O M M t^ t^
ro 0> to (N uooo O ^O PO <N
^t^w ION Ovt^-+i-(00vO
OOOOOOOMMMHIMMINMINrO'O'*^ IOM3 !>. t^OO Ov 6 O
odddddddddddddddddddddddddMw
M«iot^OOOOOOOOtnOioO>n'+OOOOi
MHt^cOOOOCSVOt^rOOlN»Ot^O<N>OOl^O>OI
OOOM-*t^O<MvOO^O> -+00 <N M M O OOC \0 m CO '
^ Tt lovO t^oo 00 O
<5 to •* CO M O^00 O '^
•*^ f^O too Looo cs ^j
M rOcO'^'OO 1^00 O
0>0 't (
O) O CO 1
CO -*<> 1
I O O O OOO f-
O to O O O O I
to t^ O to O to I
Ov cOOO M to CO '
o o o o o o
o o o o o o
CO O r^ ^00 00
O O 00 t^vo vO to to ■^ CO '
00 00 00 oo t^ t^ t^ t^O 'O to 1
OOvMrototot^O^cor^O^i _ _--
OOHWMMMMCSMOtOCOCO^'^tO tO^O t^ t^OO d I
oooooooooooooooqqoqqqqqwHMHM
6666666666666666666666666666
lo to o to o o
M M CO CO CO
■ too
O 00 t^ to •
OvO coo 'l-CO <N O O 'too <N \D O
\0 p^ CO f^ ^ M O^O ^ M p^O CO M
C> C-- io\0 00 O M 00 t^t-t^OOO
CO ^ too t^ O O w CO to 1
O O O O O O w
ddddd ddoooooboooooooooooo
OOO r^O r}- CO <N M
. _ . .C^^-to<NOooOT^csOoO
Mi-(C-)c<<scococo^ too t^ t^oo O O M M
ROLLED THREADS
23
ROLLED THREADS
The rolled thread process dates back more than 50 years and was
first patented in England. It was first used on comparatively rough
work such as track bolts but has come to be used on such fine work
as the sizing of taps and screws for micrometers.
The thread is forced up into the dies so that the finished screw is
larger than the original wire by about the depth of one thread. In
this way the size of the wire to use for any screw may be found by
subtracting the depth of one thread from the outside diameter of
the screw. This is
.866
Exact allowance depends on
threads per inch
material being roUed and other conditions.
The dies are usually flat plates of steel, having grooves of the same
pitch and shape as the thread to be rolled. The dies can be easily
laid out as follows:
Draw a horizontal line equal in length to the circumference of the
wire or blank, and at its end draw a vertical line equal to the lead of
the screw. The diagonal line made by joining these two points shows
the angle of incline of the grooves. This can be done more easily if
both the circumference and the pitch are laid out to ten times their
actual dimensions.
Dimensions of Blanks for U. S. S. Rolled Thread Screws
(Reed & Prince Mfg. Co.)
Size
T. P. 1.
A
•Size
T. P. 1.
A
i
40
.1074
.1054
T^6
12
•5063
•5031
3
.1586
5
.5638
16
24
.1566
8
•5605
i
20
•2157
•2137
3
4
10
.6828
.6794
A
18
2745
.2715
i
9
.8006
.7972
1
16
•3325
•3295
I
8
.9165
•9131
7,
.3890
-r 1
1.0298
i¥
14
.3860
Is
7
1.0262
h
13
.4480
•4450
li
7
1. 1548
1.1512
24
SCREW THREADS
ACME 29° SCREW THREADS
=No. of "Threads per Jnoh.
.D=.5P+.01
7 =.3707 P
'W=.3707P— .0058
S=.0293 P
B==.6293P f .0052
The Acme standard thread is an adaptation of the most com-
monly used style of Worm Thread and is intended to take the place
of the square thread.
It is a little shallower than the worm thread, but the same depth
as the square thread and much stronger than the latter.
The various parts of the Acme standard thread are obtained as
follows:
Width of Point of Tool for Screw Thread =
.^707
. ^J—L _ .0052.
No. of Threads per inch
.^707
Width of Screw or Nut Thread
Diameter of Screw at Root =
Diameter of Screw
No. of Threads per inch
-+.020^.
Depth of Thread
No. of Threads per inc
I
+ .010.
2 X No. of Threads per inch
Table of Acme 29° Screw Thread Parts
N
P
D
F
W
S
B
Width of
Width T
Number of
Pitch of
Depth of
Width of
Space at
of Space
at Root
Threads
Single
Thread
^°p °i
Bottom of
at Top of
of .
per Inch
Thread
Thread
Thread
Thread
Thread
I
I.O
.5100
•3707
•3655
.6293
6345
li
•750
•3850
.2780
.2728
.4720
4772
2
.500
.2600
.1853
.1801
.3147
3199
3
■Z2>ZZ
.1767
•1235
.1183
.2098
2150
4
.250
•1350
.0927
.0S75
•1573
1625
5
.200
.1100
.0741
.06S9
.1259
1311
6
.1666
•0933
.0618
.0566
.1049
IIOI
7
.1428
.0814
.0529
.0478
.0899
0951
8
.125
.0725
.0463
.0411
.0787
0839
9
.1111
•0655
.0413
.0361
.0699
0751
10
.10
.0600
•0371
.0319
.0629
0681
ACME 29° TAP THREADS
25
ACME 29° TAP THREADS
UpL^-s — >| I
N =No. of Threads jwr Inoh'
P==-^ = Linear Pitch ™
W=.3"07P— .0052
S = .C293P+.0O52
B =.8293 P +.0052
t
The Acme standard tap-thread is cut with the same width of tool
as the screw -thread and the diameter at the root is the same for tap and
screw. Clearance at bottom of thread between screw and nut is
obtained by boring the nut blank .020 oversize.
The outside diameter of the tap is made .020 larger than the screw
to give clearance between top of screw-thread and bottom of nut.
Width of Point of Tool for Tap-Thread =
.3707
Width of Thread
No. of Threads per Inch
.3707
.0052.
No. of Threads per Inch
Diameter of Screw + .020,
.0052
Diameter of Tap
Diameter of Tap at Root =
\No. of Threads per Inch
+ .040.
Depth of Thread
2 X No. of Threads' per Inch
Table of Acme Standard 29° Tap-Thread Parts
+ .020.
N.
P
D
F
W
S
B
Number of
Threads
per Inch
Pitch of
Single
Thread
Depth of
Thread
Width of
Top of
Thread
Width of
Space at
Bottom of
Thread
Width
of Space
at Top of
Thread
Thickness
at Root
of Thread
I
li
2
3
4
1
7
8
9
10
I.O
.750
.500
.250
.200
.1666
.1428
.125
.nil
.10
.5200
•3950
.2700
.1867
.1450
.1200
.0914
.0825
•0755
.0700
.3655
.2728
.1801
.1183
.0875
.0689
.0566
.0478
.0411
.0361
.0319
.3655
.2728
.1801
.1183
.0875
.0689
.0566
.0478
.0411
.0361
0319
.6345
.4772
.3199
.2150
.1625
.1311
.1101
.0951
.0839
■0751
.c68i
•6345
.4772
•3199
.2150
.1625
.1311
.1101
.0951
.0839
.0751
.0681
26
SCREW THREADS
Brown & Sharpe Screw Thread Micrometer Caliper
Readings
READING OF CALIPER
ForU. S. Threads =D
•6495
U. S. Standard Threads
s
.2
P
Pitch
Caliper
Reading
i
Ktch
Caliper
Reading
D
P
D -^IfS
.6495
D
P
J) -6495
•649s
P
P
P
P
64
.0101
\
20
.2176
.0324
62
.0105
♦
18
.2765
.0360
60
.0108
t
16
•3344
.0406
58
.0112
tV
14
•3911
0464
56
.0116
\
13
.4501
.0499
54
.0120
^>
12
.5084
.0541
52
.0125
1 •
II
.566
.0590
50
.0130
f
10
.6851
.0649
48
.0135
I
9
.8029
.0721
46
.0141
8
.9188
.0812
44
.0148
U
7
1.0322
.0928
42
.0155
I ^
7
1-1572
.0928
40
.0162
1 1
6
1.2668
.1082
38
.0171
I J
6
1.3918
.1082
36
.0180
If
5i
1-507
.1180
34
.0191
1 1
5
1. 6201
.1299
32
.0203
1 1
5
1-7451
.1299
30
.0217
2
4i
1-8557
.1443
28
.0232
2i
4
2-3376
.1624
26
.0250
3
3i
2.8145
.1855
24
.0271
3i
3i
3.3002
.1998
22
.0295
4
3
3-7835
.2165
As there is no standard of diameter for the finer pitches, the col-
umns for diameter and caliper reading are left blank. The column
on the right gives the number to be subtracted from the diameter to
obtain the caliper reading.
For explanation of screw thread piicrometer caliper, refer Xc
page 28*
THREAD MICROMETER READINGS
27
Brown & Sharpe Screw Thread Micrometer Caliper
Readings
READING OF CALIPER
For "V" Threads =D -
.866
'*V" Threads
i
Pitch
CaUper
Reading
S
P
Pitch
Caliper
Reading
.866
.866
^ .866
.866
D
P
D ^
-— -
D
p
D ^
P
P
P
"F
64
•0135
i
24
.2139
.0361
62
.0140
i
20
.2067
.0433
60
.0144
i^E
20
.2692
.0433
58
.0149
fa
18
.2644
.0481
56
•0155
f
18
.3269
.0481
54
.0160
I
16
.3209
.0541
52
.0167
7
T6
16
•3834
.0541
SO
.0173
tV
14
.3756
.0619
48
.0180
h
14
.4381
.0619
46
.0188
h
13
•4334
.0666
44
.0197
h
12
.4278
.0722
42
.0206
♦
14
.5006
.0619
40
.0217
T%
12
•4903
.0722
38
.0228
f
II
•5463
.0787
36
.0241
10
.5384
.0866
34
.0255
H
10
.6009
.0866
32
.0271
f
10
.6634
.0866
30
.0289
7
9
.7788
.0962
28
.0309
I
8
.8918
.1082
26
'032,3
li
8
1.0168
.1082
li
7
1. 1263
.1237
I§
6
1-3557
.1443
As there is no standard of diameter for the finer pitches, the col-
umns for diameter and caliper reading are left blank. The column
on the right gives the number to be subtracted from the diameter to
obtain the caliper reading.
For explanation of screw thread micrometer caliper, refer to
page 28i
28
SCREW THREADS
Brown & Sharpe Screw Thread Micrometer Caliper
Readings
reading or caliper
For Whitworth Threads = D —
.640
Whitworth Standard Threads
Diam.
Pitch
Caliper Reading
D
P
.640
.640
P
P
^
20
.2180
.0320
A
18
.2769
•0355
I
16
.3350
.0400
14
.3918
•0457
h
12
.4467
•0533
■3^
12
.5092
•0533
f
II
.5668
.0582
"li
11
.6293
.0582
^
10
.6860
• .0640
^
,10
.7485
.0640
i
9
.8039
.0711
U
9 .
.8664
.0711
8
.9200
.0800
u
7
1.0336
.0914
7
I.1586
.0914
6
1.2684
.1066
2
6
1-3934
.1066
If
5
1.4970
.1280
5
1.6220
.1280
ll
4^
1.7328
.1422
2
4I
1.8578
.1442
2|
4i
1.9828
.1422
SCREW-THREAD MICROMETER CALIPER
The Brown & Sharpe thread micrometer is fitted with pointed
spindle and "V" anvil as in Fig. 10, to measure the actual thread
on the cut surface. Enough of the point is removed and the bottom
of the "V" is carried low enough so that the anvil and spindle clear
the top and bottom of the thread and rest directly on the sides oi
the thread.
MEASURING SCREW-THREAD DIAMETERS 29
As it measures one-half of the depth of the thread from the top,
on each side, the diameter of the thread as indicated by the caliper,
or the pitch diameter, is the full size of the thread less the depth of
one thread.
This depth may be found as follows;
Depth of V threads = .866 -~ number of threads to i"
" " U. S. Std. " = .6495 ^ " " " " "
" "Whitworth " =.64 -f- " « « « "
KZ3
Fig. 10. — Spindle and Anvil of Thread Micrometer
As the U. S. thread is flatted | of its own depth on top, it follow^s that
the pitch diameter of the thread is increased I on each side, equaling
J of the whole depth and instead of the constant .866 we use the
constant .6495, which is | of .866.
When the point and anvil are in contact the o represents a line
drawn through the plane A B, Fig. 10,
and if the caliper is opened, say to .500, it represents the distance
of the two planes .500" apart. The preceding tables are used in
connection with the micrometer.
MEASURING EXTERNAL SCREW-THREAD DIAMETERS
WITH MICROMETERS AND WIRES
It is frequently necessary, especially in making a tap or thread-
plug gage, to measure the thread diameter on the thread angle in
addition to measuring on top of the thread and at the bottom of the
thread groove, and unless calipers made expressly for such work are
at hand, the measurement on the thread angle is not made with any
degree of accuracy or is omitted entirely. The accompanying
sketches, Figs. 11, 12 and 13, formulas, and tables, are worked out
for convenience in screw-thread inspection, so that by using ordi-
nary micrometer calipers and wire of the diameter called for in the
table the standard threads can be compared with the figures given.
Threads of Special Diameter
For threads of special diameter the values of x, Xi or X2 can be
readily computed from the formula corresponding to the method of
measuring to be used. The method shown in Fig. 11 at :x: is liable
to lead to an error unless care be taken that the diameter on top of
the thread is correct, and also that the flatted surface on the top of
the threads is concentric with the rest of the thread. The concen-
tricity of the flatted surface can be tested by measuring, as at x, Fig.
II, at several points on a plane through the axis and at right angles.
to it. The wire used must be round and of uniform diameter.
30
SCREW THREADS
fl P xa
Fig. II. — Measuring U. S. Standard Threads
D = outside diameter of thread.
Di = root diameter measured in thread groove.
n = number of threads per inch of length.
d = depth of thread.
p = distance from center to center of adjacent threads.
/ = width of flat on U. S. Standard thread.
a = diam^eter of wire used.
B = distance from apex of thread angle at root, to center of wire,
Z>2= diameter of cyHnder touched by apexes of thread angles.
X = diameter from top of threads on one side of tap or bolt, to
top of wire laid in thread groove on opposite side.
U. S. Standard Thread
lead = - , for single threads.
^x. 6495 =-5^.
l = i/(Z? -2J)2+ ^
Iead\^
from p, max; to /> X .505, min.
B =
Z)2=r> -
1-5155
D D2 ^ a
X =- + —' + 5 + -,
22 2
Xi — D2+ 2 B -\- a.
s/
(D2 + 2 5)2 +
('f5>
MEASURING SCREW-THREAD DIAMETERS
31
Table for Measuring U. S. Standard Threads with Microm-
eters AND Wires
D
n
D,
Da
a
B
C^y
X
Xl
X2
K
20
.1867
.1742
.04
.04
.000625
.2721
.2942
.2955
lY
18
.2419
.2283
.04
.04
.000771
-3304
-3483
•3495
r
16
.2954
.2803
.04
.04
.000976
.3876
.4003
.4016
tV
14
.3465
.3292
.04
.04
.001274
.4433
.4492
•4507
V
13
.4019
.3834
.06
.06
.001479
•5317
.5634
•5647
A'
12
.4561
.4362
.06
.06
.001735
.5893
.6162
.6177
r
II
.5089
.4872
.06
.06
.002065
.6461
.6672
.6681
ir
II
•5712
.5497
.06
.06
.002065
.7086
-7297
-7312
r
10
.6221
.5984
.06
.06
.0025
-7643
-7784
.7801
w
10
.6844
.6609
.06
.06
.0025
.8267
.8409
.8425
K
9
.7327
.7066
O.IO
O.IO
.003086
.9408
1.0066
1.0083
w
9
•7950
.7691
O.IO
O.IO
.003086
1.0033; 1. 0691 j 1.0706
i"
8
.8399
.8105
O.IO
O.IO
.003906
I.0553JI.II05II.II24
iV
7
.9421
.9085
O.IO
O.IO
.005102
I.I667JI.2085II.2I07
li"
7
1.0668
1-0335
0.10
O.IO
.005102
I.29I7
^'3335
I-335S
ir
6
1.1614
1. 1224
O.IO
O.IO
.006944
1-3987
1.4224
1.4250
ir
6
1.2862
1.2474
O.IO
O.IO
.006944
1-5237
1-5474
1-5497
ir
5^
1-3917
1-3494
0.15
0.15
.008263
1. 7122
1.7994
1.8019
ir
5
1.4935
1.4469
0.15
0.15
.010
1.8234
1.8969
1.8997
ir
5
1.6182
1-5719
0.15
0.15
.010
1.9484
2.0219
2.0245
2"
4l
1.7149
1.6632
0.15
0.15
.012343
2.0566
2.1132
2.1163
2Y
4i
1-8393
1.7882
0.15
0.15
.012343
2.I8I6
2.2382
2.2411
^Y
4l
1. 9641
1.9132
0.15
0.15
.012343
2.3066
2.3632
2.3667
2%"
4
2.0540
1.9961
0.15
0.15
.015625
2.4105
2.4461
2.4495
2V
4
2.1787
2.1211
0.15
0.15
.015625
2.5355
2.5711
2.5742
2r
4
2.4284
2.3711
0.15
0.15
.015625
2.7855
2.8211
2.8240
<.
^f
2.6326
2.5670
0.20
0.20
.020392
3.0835
3.1670
3-1704
zY
3f
2.8823
2.8170
0.20
0.20
.020392
3-3335
3.4170
3.4200
zY
3i
3.1041
3-0337
0.20
0.20
.023654
3.5668
3-6337
3.6368
zk"
3
3-32II
3.2448
0.20
0.20
.02775
3-7974
3-8448
3.8486
4"
^.
3.5708
3.4948
0.20
0.20
.02775
4.0474
4.0948
4.0983
4i*
2r
3.8019
3.7228
0.20
0.20
.03024
4.2864
4.3228
4.3264
aY
2r
4.0318
3.9489
0.20
0.20
.03305
4.5244
4-5500
4.5530
aV
2r
4.2592
4.1728
0.20
0.20
.03625
4.7614
4-7728
4.7767
5"
2^
4.4848
4.3938
0.20
0.20
.040
4.9970
4-9938
4.9980
5Y
2^
4.7346
4.6438
0.20
0.20
,040
5.2470
5-2438
5-2477
€
2r
4.0574
4.861Q
0.20
0.20
.04431
5.4810
5.4619
5.4661
If
2r
5.2072
5.1119
0.20
0.20
.04431
5.7310
5.7119
5.7160
6"
2Y
5.4271 5.3264
0.20
0.20
.049373
5.9632
5.9264
5.9307
32
SCREW THREADS
k^-a-->|
Fig. 12. — Measuring 6o-Degree V-Threads
D — outside diameter of thread.
D\ = root diameter measured in thread groove.
n = number of threads per inch of length.
d = depth of thread.
p = distance from center to center of adjacent threads.
a = diameter of wire used.
B = distance from apex of thread angle at root, to center of wire.
i?2= diameter of cyHnder touched by apexes of thread angles.
X — diameter from top of threads on one side of tap or bolt, to
top of wire laid in thread groove on opposite side.
60° V Thread
P = lead = - , for single threads.
n
n
.866
, max; to p X -577, min.
2
Do^D -
sin 30° = a.
1.732
2 2 2
Xi
X2
D2+ 2B + a.
/
iD,+ 2Br+(^-^y + a.
MEASURING SCREW-THREAD DIAMETERS
33
Table for Measuring 6o-Degree V-Threads with Microm*
ETERS AND WiRES
D
n
Di
D3
a
B
Cfy
X
Xl
X2
i"
20
.1653
.1634
0.04
0.04
.000625
.2667
.2834
.2846
tV
i8
.2180
.2163
0.04
0.04
.000771
.3244
.3363
.3375
r
i6
.2685
.2667
0.04
0.04
.0009765
.3808
.3867
.3881
tV
14
.3158
.3138
0.06
0.06
.0001274
.4656
.4938
.4957
r
12
•3580
.3557
0.06
0.06
.001735
.5178
•5357
•5375
^^
12
.4202
.41S2
0.06
0.06
.001735
.5803
.5982
.5998
r
II
.4697
.4676
0.06
0.06
.0020657
.6363
.6476
.6492
w
II
.5319
•530
0.06
0.06
.0020657
.6987
.7100
.7115
r
lO
.5789
.5768
O.IO
O.IO
.0025
.8134
.8768
.8784
w
lO
.6412
.6393
O.IO
O.IO
.0025
.8759
•93^3
.9413
r
9
.6847
.6826
O.IO
O.IO
.003086
.9288
.9826
.9843
w
9
.7470
.7450
O.IO
O.IO
.0030S6
.9912
1.045
1.0466
i"
8
.7859
.7835
O.IO
O.IO
.003906
I.04I7
1.0835
1.0854
ir
7
.8803
.8776
O.IO
O.IO
.005102
I.I5I3
1.1776
1. 1800
iV
7
1.0050
1.0026
O.IO
O.IO
.005102
1.2763
1.3026
1.3047
i¥
6
1.0895
1.0S63
0.15
0.15
.006944
1.4556
1.5363
1.5388
,l«r
6
1.2141
1.2113
0.15
0.15
.006944
1.5806
1.6613
1.6635
_5/r
5
1.2825
1.2786
0.15
0.15
.010
1.6768
1.7286
1.7317
J 4*
5
1.407:
1.4036
0.15
0.15
.010
I.80I8
1.8536
1.8565
Tr
4i
1.4941
1.490
0.15
0.15
.012343
1-9075
1.9400
1.9434
2"
4^
1.6188
1. 615
0.15
0.15
.012343
2.0325
2.0650
2.0682
21"
4l
1-7435
1.740
0.15
0.15
.012343
2.1575
2.1900
2.1930
2V
4^
1.8683
1.8651
0.15
0.15
.012343
2.2S25
2.3150
2.3178
21"
4h
1.9930
1.990
0.15
0.15
.012343
2.4075
2.440
2.4426
2V
4
2.0707
2.067
0.20
0.20
.015625
2.5835
2.670
2.6670
2i"
4
2.3203
2.317
0.20
0.20
.015625
2.8335
2.917
2.9196
3"
3^
2.5089
2.505
0.20
0.20
.020392
3.0525
3.105
3-1085
3V
3h
2.7587
2.755
0.20
0.20
.020392
3.3025
3-355
3-3582
3r
3i
2.9711
2.967
0.20
0.20
.023654
3.5335
3.567
3-5705
•sr
3
3.1770
3-1727
0.20
0.20
.02775
3.7613
3.7727
3-7765
4"
3
3.4266
3.4227
0.20
0.20
.02775
4.01 13
4.0227
4.0263
WATCH SCREW THREADS
Wai
CH SCI
ew threads are of sharp V-form and gener
ally 45-degree
angle f
or sen
iws used in nickel and brass; though 60 d
egrees for use
in stee
I. Th
e Waltham Watch Company and others
use the centi-
meter
as the
unit for all measurements with the exc
eption of the
pitch,
which
is based on the inch; the Waltham three
ds being no,
I20, I^
^o, 1 6c
), 170, 180, 200, 220, 240, 254, per inch £
md the diam-
eters r
anging
from <
3. 1 20 t(
> 0.03
5 cm.
34
SCREW THREADS
I* -a. J
Fig. 13. — Measuring Whitworth Threads
D = outside diameter of thread.
Di= root diameter measured in thread groove.
n = number of threads per inch of length.
d = depth of thread.
p = distance from center to center of adjacent threads.
r = radius on Whitworth thread.
a = diameter of wire used.
B = distance from apex of thread angle at root, to center of wire.
D2= diameter of cylinder touched by apexes of thread angles.
X — diameter from top of threads on one side of tap or bolt, tc
top of wire laid in thread groove on opposite side.
Whitworth Thre.\d
p
= lead = -, for single threads.
d
= ^X.64033=^^-
Di
..0z._,,)3 + (l£^y.
r
-PX .1373-
a
= p X .84, max; to ^ X -454, min.
B
= - -T- sm 27° 30' = -.
2 ' ^ .9235
D.
1.600825
2 2 2
D2+ 2B + a.
~^(D,+ .By + (l^'y +
a.
MEASURING SCREW-THREAD DIAMETERS
35
Table tor Measuring Whitworth Threads with Micrometers
AND Wires
D
n
Di
D2
a
B
(^!r
X
Xl
X2
r
20
.1875
.1699
0.04
•04331
.000625
.2733
•2965
•2977
■h"
i8
.2428
.2235
0.04
•04331
.000771
•3313
•3501
•3514
¥
i6
.2965
.2749
0.04
.04331
.000976
'3^^?>
.4015
.4029
iV
14
.344
•3231
0.04
•04331
.001274
.4436
.4497
.4512
¥
12
•3953
.3666
0.06
.06496
.001735
•5232
.5563
.5582
rV
12
•4576
.4291
0.06
.06496
.001735
•5907
.6190
.6204
r
II
.5105
•4794
0.06
.06496
.002065
•6372
.6693
.6710
w
II
.5728
.5420
0.06
.06496
.002065
.7097
•7319
•7334
r
lO
.6239
.5899
0.06
.06496
.0025
.7649
.7798
.7815
w
lO
.6862
.6524
0.06
.06496
.0025
.8274
.8423
.8438
V
9
.7348
.6971
0.06
.06496
.003086
.8810
.8870
.8882
w
9
.797
•7596
C.06
.06496
.003086
•9435
.9495
.9512
/r
8
.8422
.7999
O.IO
.I0S39
.003906
1.0583
1.1167 1.1185
ir
7
.9447
.8963
O.IO
.I0S39
.005102
1. 169
1.2131
1. 2153
ir
7
1.0693
1.0213
O.IO
.10839
.005102
1.294
1.3381
1.340
ir
6
1. 1644
1. 1082
O.IO
.10839
.006944
1.400
1.4250
1.4276
iV
6
1.2892I1.2332
O.IO
.I0S39
.006944
1.525
i.55ooli.5523
ir
5
1. 3 7 26] 1. 3 048
0.15
.16242
.010
1.7023
1. 7796'!. 7826
iV
5
1.497
1.4298
0.15
.16242
.010
1.8273
1.9046 1.9074
T 'f
a\
1.5942
1-5193
0.15
.16242
.012343
1-9345
1.9941
1-9973
2"
4i
1.7185
1.6443
0.15
.16242
•012343
2.0595
2.1191
2.1221
2Y
4i
1-8437
1.7693
0.15
.16242
•012343
2.1845
2.2441
2.2470
2V
4
1-9338
1.849S
0.15
.16242
.015625
2.2873
2.3246
2.328
2r
4
2.0585
1-9750
0.15
.16242
.01562512.4123
2.4498
2-453
2¥
4
2.1833
2.100
0.15
.16242
.015625 2.5373
2.5748
2.5778
2r
3l
2.3882
2.2926
0.20
.21567
.020392 2.837
2.9240
2.9276
s'^
3i
2.6397
2.5426
0.20
-21567
.020392 3.087
3.1740
3-1773
3r
3i
2.860
2-7574
0.20
.21567
.023654 3.3194I3.3887
3-3924
3r
3i
3.1098
3.0074
0.20
.21567
.02365413.5694,3.6387
3.642
sr
3
3.327
3.2164
0.20
-21567
.027755
3-799
3.8477
3.8515
4^
3,
3.5768
3.4664
0.20
.21567
.027755
4.049
4.0977
4.1012
4r
2|
3.808
3-693
0.20
-21567
.030241
4.287
4.3243
4-328
4r
2f
4.0582
3.943
0.20
-21567
.030241
4-537
4-5743
4.578
4f
2f
4.2878
4.168
0.20
.21567
-033051
4.7746
4-7993
4.8025
S"
2f
4-5376
4.418
0.20
.21567
.033051
5-0245
5.0493
5.0524
sY
- 2f
4-7658
4.640
0.20
.21567
.036252
5.2607
5.2713
5.275
S¥
2|
5-0156
4.890
0.20
.21567
.036252
5-5107
5-5213
5-5248
sr
2j
5-2415
5. no
0.20
.21567
.040
5-7455
5-7413
5-7446
6"
2\
5-4913
5-360
0.20
.21567
.040
5-9955
5.9913
5-9944
36
SCREW THREADS
MEASURING FINE PITCH SCREW-THREAD
DIAMETERS
The accompanying table should be of service to those using the
three-wire system of measurement as the constants cover the finer
pitches and may be easily applied to screw threads of any diameter.
The diagrams, Fig. 14, make the method of application so plain
that no description appears necessary.
Formulas:
For V Thread For Sellers Thread
D = (M - 3 W) + 1.732 P. D = (M - 3 W) + 1. 5155 P.
M = (D - 1.732 P) + 3 W. M = (D - 1.S155 P) + 3 W.
Fig. 14. — Measuring Fine Pitch Threads
Constants for Use with the 3-W1RE System of Measuring
Screw Threads
Threads
per Inch
For
V Thread
1.732 P =
For SeUers
Thread
1.515s P=
Threads
per Inch
For
V Thread
1.732 P =
For Sellers
Thread
1-5155 P =
8
.21650
.18943
25
.06928
.06062
0
.19244
.16839
28
.06185
.05412
10
.17320
.15155
32
.05412
.04736
II
•15745
•13777
36
.04811
.04210
12
.14433
.12629
40
.04330
.03789
13
.13323
.11658
48
.03608
.03157
14
.12371
.10825
50
.03464
.03031
16
.10825
.09472
56
.03093
.02706
18
.09622
.08419
64
.02706
.02368
20
.08660
.07578
80
.02165
.01894
22
.07872
.06889
100
.01732
.01516
24
.07216
.06314
MEASURING METRIC THREADS
37
* MEASURING METRIC SCREW THREAD
DIAMETERS
The tables and formulas given herewith in connection with Fig. 15
should be of value to those engaged in work requiring the frequent
production of thread gages or special taps in the metric sizes. The
three wire system is used as in the preceding tables, the wires being
appHed as indicated.
Formulas:
For V Threads
D = (M - 3 W) + 1.732 P.
M = (D - 1.732 P.) +3W.
For Threads with Flat Top
and Bottom equal to 5 of
the Pitch
D = (M -3W) +1.SISS P.
M = (.D - i.siSS P.) 4- 3 W.
Fig. 15. — Measuring Metric Threads
Constants for Use in Measuring Metric Screw Threads
BY the 3-W1RE System
Pitch
m-m
Pitch
Inches
1.732P
I-5I55P
Pitch
m-m
Pitch
Inches
1.732P
t.5i55P
o.S
0.75
I.O
.01969
•02953
.03937
.03410
.05109
.06819
.02984
•04475
.05966
4.5
5.0
5-5 •
.17717
.19685
.21654
.30686
.34094
•37500
.26850
29833
32816
1.25
1-5
1-75
.04921
.05900
.06890
.08523
.09719
• 11933
.07458
.08941
.10442
6.0
6.5
7.0
.23622
•25591
•27559
.40913
•43773
.47677
38783
41766
2.0
2.5
30
.07874
.09843
.11811
.13638
.16948
.20456
•11933
.14917
.17899
7-5
8.0
9.0
.29528
•31496
•35433
•51092
.54551
.60870
44749
47732
53699
3-5
4.0
.13780
•15748
.23867
.26775
.20784
.23866
10.00
.39370
.68189
5966s
3^
SCREW THREADS
MEASURING ACME 29-DEGREE THREADS
The diameter of a wire which will be flush with tops of thread on
tap when laid in the Acme thread groove, Fig. 16, will be found as
follows:
Rad, ci wire section = side opp. = side adj. X tan. 37° 45' =
/. X. 6.93+ -005^ ^_^^^^3,
Diam. of wire = (p X .6293 + .0052) .77428.
Wires of the diameter given in the table come flush with the tops
of tao threads and project .010 above the top of screw threads.
, Tap Thread
^ — ^ — H h-
A
Fig. 16. — Measuring Acme Threads
Table op Wire Sizes for Measuring Acme St.\ndard 29° Screw
AND Tap Threads
Threads per Inch
Pitch
Diam. of Wire
I
I.
0.4913
li
•750
0.3694
ih
.6666
0.3288
If
.5774
0.2824
2
.500
0.2476
2h
.400
0.1989
3
'3333
0.1664
4
.250
O.125S
s
.200
O.1014
6
.1666
0.0852
7
.1428
0.0736
8
.125
0.0649
9
.iiii
0.0581
10
.100
0.0527
^
MEASURING 29-DEGREE WORM THREADS 39
MEASURING BROWN & SHARPE 29-DEGREE
WORM THREADS
The diameter of wire for Brown & Sharpe worm thread, Fig. 17,
for each pitch, that will rest in the thread groove on the thread angle
and be flush with the tops of the finished threads, is found as follows;
Rad. of wire section (see table) = side opp. = side adj. X tan.
37° 46' = -^ — ^ — X 0.77428 = 0.257448 P and diam. of wire =
0.5149 P-
Fig. 17. — Measuring Brown & Sharpe Worm Threads.
Table of Wire Sizes for Measuring B. & S. 29° Worm Threads
Threads per Inch
Pitch
Diam. of Wire
h
2.
1.0298
f
1-750
0.9010
f
1.500
0.7723
1
1.250
0.6436
I
I.O
0.5149
ih
.6666
0.3432
2
•5
0.2574
2|
A
0.2060
3,
•Z333
O.1716
3i
.2857
O.1471
4
.250
0.1287
4i
.2222
O.I144
5
.2
0.1030
6
.1666
O.0S58
7
.1428
0.0735
8
.125
0.0643
9
.iiii
0.0572
ro
.10
0.0515
12
'<^^3Z
0.0429
16
.0625
0.0322
20
.050
0.0257 .
__
40
WORM THREADS
of Threads per Tnch.
= Linear Pitch
S — .665 P
B=.69P
Pitch =
Depth of Thread
No. of Threads per inch
.6866
Width of Top of Thread
Width of Space at Bottom
Clearance at Bottom of Thread
Width of Space at Top of Thread =
Thickness at Root of Thread =
No. of Threads per inch'
-335
No. of Threads per inch
.310
No. of Threads per inch
Thickness at Pitch Line
10
.665
No. of Threads per inch
.69
No. of Threads per inch
Table of Brown & Sharpe 29° Worm Thread Parts
P
D
F
w
T
A
c
s
B
III
2^
111
•5 82
mi
"1
e £ S
-0%
•5 S 0
III
I
I.O
.6866
•3350
.3100
.5000
.3183
•05
.66=;
.69
li
.8
•5492
.2680
.2480
.4000
.2546
.04
.532
.552
li
.6666
•4577
.2233
.2066
•3333
.2122
•0333
•4433
•4599
2
•5
•3433
•1675
.1550
.2500
.1592
.0250
.3325
.345
2i
.4
.2746
.1340
.1240
.2000
.1273
.0200
.2660
.276
3
'3333
.2289
.1117
•1033
.1666
.1061
.0166
.2216
.2299
3i
.2857
.1962
•0957
.0886
.1429
.0909
.0143
.1901
.2011
4
.250
.1716
.0838
•0775
.1250
.0796
.0125
•1637
.1725
4i
.2222
.1526
.0744
.0689
.IIII
.0707
.GUI
.1478
•1533
5
.2
•1373
.0670
.0620
.1000
.0637
.0100
'^330
.138
6
.1666
.1144
.o55«
•0517
.0833
•0531
.0083
.1108
.115
7
.1428
.0981
.0479
.0443
.0714
•04S5
.0071
•095
.0985
8
.125
.0858
.0419
.0388
.0625
.0398
.0062
.0818
.0862
9
.iiii
.0763
.0372
•0344
.0555
•0354
•0055
.0739
.0766
10
.10
.0687
•0335
.0310
.0500
.0318
.005
.0665
.069
12
.0833
.0572
.0279
.0258
.0416
.0265
.0042
•0551
.0575
16
.0625
.0429
.0209
.0194
.0312
.0199
.0031
.0409
.0431
20
r
.050
•0343
.0167
.0155
.0250
.0159
.0025
.0332
.0345
WORM WHEEL HOBS
41
WORM WHEEL HOBS
Hobs are made larger in diameter than the worm they are used
with by the amount of two clearances. The Brown & Sharpe method
is to make the clearance one-tenth of the thickness of the tooth on
the pitch line or .05 inch for a worm of one pitch. If the worm was
3 inches oulside diameter, which would be a fair proportion for this
pitch, the outside diameter of the hob would be 3 + (2 X .05) = 3.1
inches. The thread tool would be .31 inch wide at the point and
would cut .6366 -f .1 = .7366 deep, leaving the top of the thread
the same thickness as the bottom, which is different from the worm.
The land L should be made as near the proportions given as pos-
sible.
A = .G9xPitch
B = .3Ix Pitch.
C = VlO ofT
£ = .C9xPitch=A
J = .3683xPitcn
S=.368SxKtch
T = .5 X Pitch
~W=.31 X Ktch=I
■W.D=.7366x.Htcli
D =Diam. of Worm + !
L = WD + i^inoh
WD=.7366xHteh
Fig. 18. — Section of Hob Thread Fig. 19. — End View of Hob
The diagram Fig. 18 shows the shape and proportions of the thread
of a worm hob, and Fig. 19 shows the proportions for the depth of
tooth, the lead and the oulside diameter. In these diagrams:
A = Width of space at top of tooth.
B = Width of thread at top.
C = Clearance or difference between the hob and worm.
D = Diameter of hob.
E = Width of tooth at bottom.
F = Hight above pitch line;
L = Width of land or tooth at bottom.
'S' = Depth below pitch line.
T = Width at pitch line.
W = Width of space at bottom.
WD = Whole depth of tooth.
Brown & Sharpe allow clearance at the point of the tooth only
lor worm wheels, but at both point and bottom when bobbing
spur gears.
PIPE AND PIPE THREADS
BRIGGS STANDARD PIPE THREADS
The particulars in the following paragraph regarding this system
of pipe standards are from a paper by the late Robert Briggs, C.E.,
read in 18S2, before the Institution of Civil Engineers of Great
Britain.
The taper employed has an inclination to i in 32 to the axis. The
thread employed has an angle of 60 degrees; it is slightly rounded
off, both at the top and at the bottom, so that the hight or depth of
the thread, instead of being exactly equal to the pitch X .866 is
only four-fifths of the pitch, or equal to 0.8 , ii n be the number of
i<2 in 1 of Length
Perfect Thread Top and
Bottom = (0.8 Dia.+4.8) 3
Taper of Pipe End -% per Ft.=^g per In,
Depth of Thread ( E ) = —
ThJ. per In.
li=Number of Threads per In.
Fig. 1. — Longitudinal Section of Briggs Pipe Thread
threads per inch. For the length of tube-end throughout which
the screw-thread continues perfect, the formula used is (o.S D 4- 4.8)
X -, where D is the actual external diameter of the tube throughout
11
its parallel length, and is expressed in inches. Further back, be-
yond the perfect threads, come two having the same taper at the
bottom, but imperfect at the top. The remaining imperfect portion
of the screw-thread, furthest back from the extremity of the tube,
is not essential in any way to this system of joint; and its imperfec-
tion is simply incidental to the process of cutting the thread at a
single operation.
Thread Section
The threads as produced at the pipe end in the Briggs system
are represented clearly in the longitudinal section. Fig. i.
Here the threads that are perfect at top and bottom are shown
at F, the depth being indicated at E. Back of the perfect threads
42
BRIGGS STANDARD PIPE THREADS
43
are represented the two threads with perfect bottom and flat tops
and behind these are the imperfect threads produced by the chamfer
or bell mouth of the threading die. A table giving the general
dimensions of wrought iron tubes in the Briggs system will be found
on page 40, while complete data pertaining to the thread depths,
lengths of perfect and imperfect portions, allowances for making the
joint in screwing the pipe into the fitting, gaging allowances, etc.,
are contained in the tables on pages 47 and 4g.
In cutting pipe threads with a lathe tool as in threading taper
work in general, the tool should be set at right angles to the axis
of the piece and not square with the conical surface.
Standard Dimensions of Wrought-Iron Welded Tubes
Briggs Standard
Diameter of Tubes
Screwed Ends
Thickness
of Metal
Inches
Nominal
Inside
Actual
Inside
Actual
Outside
Number of
Threads
Length of
Perfect
Thread
Inches
Inches
Inches
Inches
per Inch
: .
0.270
0.405
0.068
27
0.19
■ ■
0.364
0.540
0.088
18
0.29
f
0.494
0.675
0.091
18
0.30
J
0.623
0.840
0.109
14
0-39
f
0.824
1.050
0.113
14
0.40
1
1.048
I.315
0.134
III
0.51
i|
1.380
1.660
0.140
Hi
0.54
li
I.610
1.900
0.145
Hi
0-5S
2
2.067
2-375
0.154
Hi
0.58
2|
2.468
2.875
0.204
8
0.89
3
3.067
3-500
0.217
8
0.95
3i
3-548
4.000
0.226
8
1. 00
4
4.026
4.500
0.237
8
1.05
4l
4.508
5.000
0.246
8
1. 10
5
5-f545
5-563
0.259
8
1. 16
6
6.065
6.625
■ 0.280
8
1.26
7
7.023
7.625
0.301
8
1.36
8
7.982
8.625
0.322
8
1.46
♦9
9.000
9.688
0-344
8
1-57
10
10.019
10.750
0.366
8
1.68
* By the action of the manufacturers of wrought-iron pipe and
boiler tubes, at a meeting held in New York, May 9, 1889, a change
in size of actual outside diameter of 9-inch pipe was adopted, mak-
ing the latter 9.625 instead of 9.688 inches, as given in the table of
Briggs standard pipe diameters.
44
PIPE THREADS
The table below shows the British pipe and pipe threads, sizes
recommended by the Engineering Standards Committee.
BRITISH STANDARD PIPE THREADS
i-(
-d
Distance 01
Gage
1-
s
5 '-
(-T-d
J
-^ jj
t
Dl-vmeter
FROM
<u
a3
1
O ij
_jj rt
^x.
i»s
J3 -
End of Pipe
11^
•2S.
Hi
ll
D C3
0-^
■IP
•0^
OS
Q^o
g'o
O 4J o
3^
3*^
1^1
n
1
it
^6
le^^
.-H-
1
0 0
r
i
en
|"o«
0
•|^W
i
hi
0.383
0.046
0.337
28
3%
0.18
0.13
0.373
0.327
I
hi
0.518
0.067
0.451
19
1^6
0.22
0.16
0.506
0.439
t
i^
0.656
0.067
0.589
19
0.29
0.21
0.640
0.573
§
§1
0.825
0.091
0.734
0.29
0.21
0.809
0.718
f
ie
0.902
0.091
0.811
0.29
0.21
0.886
0-795
f
ii'.-
1. 041
0.091
0.950
0.44
0.31
1.018
0.927
1
13^2
1. 189
0.091
1.098
0.44
0.31
1. 166
1.075
I
n\
1.309
0.116
1. 193
0.44
0.31
1.286
1. 170
li
lu
1.650
0.116
1-534
0.58
0.42
1. 619
1-503
i§
iSi
1.882
0.116
1.766
0.58
0.42
1.851
1-735
If
23%
2. 116
0.116
2.000
0.73
0.52
2.077
1. 961
2
2|
2.347
0.116
2.231
0.73
0.52
2.308
2.192
2i
2|
2.587
0.116
2.471
0.80
0.57
2.544
2.801
2i
3
2.960
0.116
2.844
0.80
O.S7
2.917
3-043
2f
3i
3.210
0.116
3.094
0.95
0.68
3-159
3-293
3
3l
3.460
0.116
3-344
0-95
0.68
3-409
3.293
3i
3f
3.700
0.116
3-584
1.02
0-73
3-645
3-529
• 3i
4
3.950
0.116
3.834
1.02
3-73
3.895
3-779
3f
4i
4.200
0.116
4.084
1.02
0.73
4-145
4.029
4
4l
4.450
0.116
4-334
1. 17
0.83
4-387
4.271
4§
5
4-950
0.116
4-834
1. 17
"0.83
4-887
4-771
5
5^
5.450
0.116
5-334
I-3I
0.94
5-380
5.264
5^
6
5.950
0.116
5.834
1.46
1.04
s-872
5-756
6
6f
6.450
0.116
6.334
1.60
115
6.364
6.248
7
7§
7.450
0.128
7.322
1.60
I-15
7-364
7.236
8
8i
8.450
0.128
8.322
1-75
1-25
8.356
8.228
Q
9l
9-450
0.128
9.322
1-75
1.25
9-356
9.228
lO
loi
10.450
0.128
10.322
10
1.90
1-35
10.348
10.220
II
II i
11.450
0.160
11.290
8
1.90
1.35
11.348
II. 188
12
12 §
12.450
0.160
12.290
8
1.90
1-35
12.348
12.188
13
13 f
13.680
0.160
13.520
8
1.90
1-35
13-578
13-418
14
14 f
14.680
0.160
14-520
8
if
2.04
1.46
14.571
14.411
15
15 f
15.680
0.160
15-520
8
I -
2.04
1.46
15-571
15-411
i6
i6i
16.680
0.160
16.520
8
If
2.19
1.56-
16.563
16.403
17
17 f
17.680
0.160
17.520
8
2
2.33
1.67
17.555
17-395
i8
i8f
18.680
0.160
18.520
8
2
..33
.6,
18.555
18.395
Paper o
; pipe end
S = l^e"
to l".
W
tiitwc
rth stai
idard tl
ireads.
TAP DRILLS FOR PIPE TAPS
45
Tap Drills for Pipe Taps
The sizes of Twist Drills to be used in boring holes, to be reamed
with Pipe Reamers, and Threaded with Pipe Taps, are as follows:
Size
Pipe
Tap
BRIGGS
WHITWORTH
Size
Pipe
Tap
BRIGGS
WHITWORTH
Thread
Drill
Thread
Drill
Thread
Drill
Thread
Drill
i
27
U
28
A
If
iH
1
i
i8
u
19
II
2
III
2t\
2^\
1
i8
T%
19
^
2i
2H
i
14
H
14
H
2i
8
2t\
2||
1
14
If
2f
3
f
14
II
. 14
II
3
8
3t6
3l
I
14
ItV
3i
3i
I
iii
li
II
li
3h
8
3H
3f
li
11^
iM
II
iM
3f
4
I^
Hi
Iff
II
III
4
8
4A
4i
Metric Pipe Threads
Nominal Inside
Pipe Diameter
in Inches
Inside Pipe
Diarneter in
Millimeters
External Thfead
Diameter in
Millimeters
Internal Thread
Diameter in
Millimeters
Number of
Threads
per Inch
i
10
8.3
19
i
6-35
13
II-3
19
f
9.52
16.5
14.8
19
^
12.70
20.5
18.2
14
1
15-87
23
20.7
f
19.05
26.5
24.2
I
25.40
33
30
i|
31-75
42
39
li
38.10
48
45
If
44-45
52
49
2
50.30
59-7
56.7
2^
63-50
76
73
3
76.20
89
86
3^
88.90
101.5
98.5
4
101.60
114
III
46
PIPE THREADS
THE PIPE JOINT IN THE BRIGGS SYSTEM
The illustrations below and the tables on pages 43 and 44, repre-
sent the relation of the reamer, tap, die and testing gages in the
preparation of the Briggs pipe end and fitting preliminary to making
up the joint.
H^
Standard Ring Gage and
Plug for Testing Fittings.
Fig. 2. — Reamer, Tap, Die and Gages for Briggs Pipe Standard
The illustrations to the left in Fig. 2 show the relative distances
that the pipe reamer, tap, testing plug and pipe end are run into
the fitting in making the joint; while at the right are shown the die
and ring gage on the pipe end, and the relative diameters of the
Standard ring gage and the testing plug for the fittings.
PIPE JOINT IN THE BRIGGS SYSTEM
47
In pipe fitting the end of the pipe should always be cut to fit the
Briggs standard pipe gage. The fitting should be tapped small
in order to insure a tight joint. Theoretically the joint should be
tight when the pipe end has been screwed into the fitting a dis-
tance represented at H in the diagrams, Fig. 2 and following tables.
However, to allow for errors the thread on the pipe is actually cut
two threads beyond H. Similarly the fitting should be tapped two
threads deeper than distance H.
The following table used in conjunction with the illustrations
in Fig. 2, contains information as to length and number of perfect
and imperfect threads; distance and number of turns the pipe screws
into fitting by hand and with wrench, or the total length and num-
ber of threads of joint; ring and plug gage data for testing tools;
besides general pipe dimensions, drill and reamer sizes, etc.
Briggs Pipe Thread Table (See page 46)
Dia. of Pipe
Actual
Outside
No. of
Threads
Dia. at
End of
Dia. at
Bottom
Depth
of
Length
of
Perfect
Threads
No. of
Perfect
Nominal
Actual
per Inch
Pipe
of Th'd
Thread
Threads
Inside
Inside
A
B
C
D
E
H
r
.270"
.405"
27
•393"
•334"
.029"
.19"
5-13
1."
..364"
.540"
18
.522"
•433"
.044"
.29"
5-22
3//
.494"
-675"
18
.656"
.568"
.044"
•30"
5-4
x»
.623"
.840"
14
.815"
.701"
.057"
.39"
5-46
3.'f
.824"
1.050"
14
1.025"
.911"
.057"
.40"
5-6
/"
1.048"
1-315"
Hi
1.283"
I. I 44"
.069"
.51"
5-87
ir
1.380"
1.660"
11^
1.626"
1.488"-
.069"
.54"
6.21
ir
1. 6 10"
1 .900"
11^
1.866"
1.728"
.069"
.55"
6.33
2 "
2.067"
2.375"
Hi
2.339"
2.201"
.069"
.58"
6.67
2Y
2.468"
2.875"
8
2.819"
2.619"
.100"
.89"
7.12
z"
3.067"
3-500"
8
3.441"
3.241"
.100"
.95"
7-6
3r
3-548"
4.000"
8
3-938"
3-738"
.100"
1 .00"
8.0
4 "
4.026"
4.500"
8
4.434"
4-234"
.100"
1 .05"
8.4
4r
4.508"
5. "
8
4-931"
4.731"
.100"
1. 10"
8.8
5"
5-045"
5-563"
8
5-490"
5.290"
.100"
1. 1 6"
9.28
6 "
6.065"
6.625"
8
6.546"
6.346"
.100"
1.26"
10.08
V'
7.023"
7.625"
8
7-540"
7-340"
.100"
1.36"
10.88
8 "
7.982"
8.625"
8
8.534"
8.334"
.100"
1.46"
11.68
9 "
9.000"
9.625"
8
9-527"
9.327"
.100"
1.57"
12.56
10 "
10.019"
10.750"
8
10.645"
10.445"
.100"
1.68"
13-44
(Table Continued on Page 48)
48
PIPE THREADS
Sinj3jra'Bq3
3joj9e:
JO pua JO -BIQ
\4
0 '=t OM>0 r^M O\i0'rt-rt0 0 0
<N M ro -^O 0 -^ ON^O 10 GO CO 00
fO '^ tJOVO 00 H ^0 H IV^ M \0 M
H M M* (N CS CO ^O -^
p3sn aq o;
una JO -^la
HHHC^CSCOCO'4"
2ufa qSnojq;
spaf
-OJj Sni j
uoqDads
^
0 vo io»= kfefeifcfcs: XT} XT) \n \n loioioo
'hOOOO^'^'^oOO<n<»<n(nu-)U-)(MO><nio
MOOOO lOVOO 0 0 rJ-OvOVOMDvO <N CN H TtOO H
M M M cs c^ rororOrOiOLOLovo lovo vO -O O vO t^
spaC
-OJJ Snjj
uoqDadsui
sp.qi JO -0^
rtNiHlTXHlr^HNHlMrtle^HlN H|NrtlNiH|NiH|N O MD <N
cOoOrOrorocO^OcOTj-Tt-Tt'^Tt'^LoioqNiH -^f^.
rt- 10 10 10
sSup
joj Snjj JO
pua JO ma
S
Mi:^r^Tj--<tO*=»= ro oOcOoOoOOONt^-^roO
0 0 •^OOs-^i>-t^r^J>-iJO<>JOOioOO M ro-^O
COmtJ-OnQvOO'^ihoOOOOnOnioOO OOO ^O
CO ^<i '^9 '^^'^ ^'^T""^'?* fOOO "nJ- to >o --t -^ Q
H H H H (N CS CO CO,'^ -^ 10 \d l>-od C> M
93^0 3ai^
puB Sntd:
UO pB9iqx
JO q;Su3T:
h5
00 CO 00 i:^ r^oo 00 louoioo 0 0 0 cOiOioiOUOO
cOMt^coiOO<vOrO\Or-~OOQOOC^(M<NO)iO
0 0 0 CO -*00 Ot~^LOCOOlOO>JOOMMMI-l(N
CN t:J- tJ- u-> lovo t-^t^t^M 04 <N coco-^ lOvO t^OO 0
MHIHMMHHHHHH
3§TiO 301-3
puB Snij uo
SP.HX JO ON
vo Tf Thoo 00 cs M cooo '^
u^^^Ol-lC^<^^COOC7^ O
H cj CO -^O 00 M coo H 0 q -^00 <N M On l-^ 10 -^
r^t^t-^i>.r^i>-ododoo dNC>d d d m c^oJ fO'j-io
qouaiAVq^iAi
JO ;unoaiy
0 10 lO*= 6;S:6:&& ITJIOUOIO XTi XT) \n Q
M 0 0 0 0 "^t ""d- ■'too 0<>)<NCSC^tr>U-)<NC>CNlO
MOOOO LOlOO 0 0 'tOOVOVOMO CN C-) M -^00 H
M M H <N CS cOcococOiJOiJ-iiJOiJO iJ-)0 vo \0 VO <5 J>.
«dfl 331BX,,
sujnx JO -o^
cOcococococOcocO-^'^TtTt-'sf'tiOiO^H -^t^.
10 10 >o
puBH
Xq Sm^iij
o:)Ut SAvajog
9dlj 93UB;StQ
00 t^ CO t^ f^oo 00 loioioioioioiocoioo 0 0 0
(N M ji^coiooo C4 000 r-t^r^f^r^M t^O coO O
u^0l^^000^'^0^-l0co COOO COOO 00 00 O O CO M
MOjMcic^cO't'* 'to 0 0 t^ r^ t-^00 0 0 H (N
IH H H H
puBH ^q
Sui^-Hj o;ui
SM3J3S Sdlj
sainx JO -o^
0 Tt 'too CO M <M COOO 00000^00000
Lo r/^ M M C>0 O'tt^OOOOOOOO'tOO
CSOO C>t^coiOco<N 00 0 0 00*^000 'too
w On 0 c> M coo coo H H '^oncooj m qi^qo
rfcO'tcO't-^'t't'tlOiOlOiOOo' «>-odod O^On
3!a
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pni^ p,qx JO
qtlSuai iBiox
0
0 0 0 ^louoiococo^oO 0 0 0 cOVOiOtoiriO
ci^OO^MO^w'tt^OOOOO'NO.c^o.io
MMCOMCOrOlJOt^OfOOlJOOlOOMMHHCS
^0 00000 0 0 0 HOt^ r^OO CO ON 0 M CN CO -^
M M M M H M M W IH l-i CN CN Cq (N (N
•pa
rll*>-l|-*n|OOHlNn|-* rH|-<<lHlP< >H|M >h1C^ r-l|M
HMM(N<NCOCO'*'t 100 t^OO 0 0
M
GAGE SETS
49
GAGE SETS FOR BRIGGS PIPE AND FITTINGS
The gages manufactured by the Pratt & Whitney Company for
makers and users of pipe and fittings include three distinct sets for
each size of pipe, and these are illustrated in Fig. 3, Set No. i con-
sists of a ring and plug conforming in all dimensions to the Briggs
standard, and is known as the standard reference set. The plug
screws into the ring wnth faces flush — as indicated by the position
of the two gages. The flat milled on the plug shows the depth to
which the latter should enter the fitting to allow for screwing up with
tongs to make a steam-tight joint; the ring, of course, screws on to
the pipe flush with the end.
£>iT«XAW:xWA\WxW;«-.R3!
Set No. 2 ^^=^~=^--' Set No. 3
Working Allowance Gages. Inspection Allowance Gages.
Fig. 3. — Briggs Pipe Thread Gages
Set No. 2 — the working allowance set — consists of the plug
already described and a ring whose thickness is equal to the standard
ring less the allowance for screwing up the joint. As the plug and
ring threads are of the same diameter at the small end, the bottom
surfaces come flush when the two members are screwed together.
It will be noted that, as the plug enters the fitting only to the bottom
of the flat at the side, and the ring screws on to the pipe only far
enough to bring the outer face flush with the pipe end, there are a
few threads on, or in, the work beyond the reach of the gages; hence
with this type of gage a reasonable amount of wear may be permitted
at the end of the tap or the mouth of the die without causing the
rejection of the work.
The plug and ring in set No. 3 are inspection allowance gages,
the ring being the same in all particulars as the standard gage in
set No. I, while the plug is longer than Nos. i and 2 by an amount
equal to the allowance for screwing up for a tight joint, this extra
length being represented by the cylindrical portion at the rear of
50
PIPE THREADS
the thread cone. When the gages are screwed together the back of
the cylindrical section comes flush with the ring face and the threaded
end of the plug projects through the ring, as indicated, a distance
equal to the length of the cylinder, or the screwing-up allowance.
This plug will enter a perfect fitting until the back of the threaded
section is flush with the end of the fitting, thus testing the full depth
of the tapped thread in the same way that the standard ring gage
covers the thread on the pipe end, and at the same time showing
that the fitting is tapped to right diameter to allow the joint to screw
up properly.
NATIONAL STANDARD HOSE COUPLING
This standard' for fire hose couplings was adopted by the Na-
tional Fire Protection Association May 26, 1905 and has since been
approved and adopted by various other organizations.
Fig. 4. — National Standard Hose Coupling
Dimensions of National Standard Hose Couplings
Inside Diameter of Hose Couplings. . .
Length of Blank End on Male Part . . .
Outside Diameter of Thread, Finished
Diameter at Root of Thread
Total Length of Male End
Number of Threads per inch
Length of Female Thread
Diameter of Top of Female Thread . .
22
3
3^
^
3iV
3t
4i
2.871S
3-3763
4-0013
I
li
ij
7i
6
6
8
I
I
30925
3-6550
4.28
4i
i
5l
5-3970
i|
4
li
5-80
Note: — The above to be of the 60-deg. V-thread pattern with one-hundredth
inch cut off the top of thread and one-hundredth inch left in the bottom of the 2i-inch,
3-inch, and sJ-inch couplings, and two hundredths inch in like manner for the 4j-
inch couplings, and with one-quarter inch blank end on male part of coupling in
each case; female ends to be cut ^-inch shorter for endwise clearance. They should
also be bored out .03 inch larger in the 2i-inch, 3 and 3|-inch sizes, and .05 inch
larger on the 4j-inch size in order to make up easily and without jamming or
Sticking.
TWIST DRILLS
The twist-drill is perhaps one of the most efficient tools in use as,
although one half is cut away in the flutes, it has a very large cutting
surface in proportion to its cross-sectional area. This is made possible
by the fact that the work helps to support the drill and the feed
pressure on the drill tends to force the point into a cone-shaped hole
which centers it.
In addition to the radial relief or backing-off behind the cutting
edge, twist -drills have longitudinal clearance by decreasing the diam-
eter from the point toward the shank, varying from .00025 to .0015
per inch of length. This prevents binding and is essential in accurate
drilling.
To increase the strength the web is increased gradually in thickness
from the point toward the shank by drawing the cutters apart. This
decreases chip room and to avoid this defect the spiral is increased in
pitch and the flute widened to make up the chip room.
PIG. I FIG. 2 FIG. 3
Grooves of Twist Drills
The shape of the groove affects the power and the shape of the
chip and experiments by the Cleveland Twist-Drill Company are
interesting. The groove in Fig. i does not give a good cutting edge,
especially near the center, as it does not allow a full curl to the chip.
Fig. 2 is a very free cutting-groove, the chips curl up to the full size
of the groove and this reduces the power required to bend the cnips.
Fig. 3 js an even better form as it rolls a chip with each turn conical
so that one lays inside the other and makes a much shorter chip
from the same depth of hole.
The angle of spirals varies from 18 to 35 degrees according to the
ideas of the maker. In theory the finer the pitch or the greater the
angle, the easier it should be to cut and curl the chip. But this
gives a weak cutting edge and reduces the ability to carry off the
heat, and it does not clear itself of chips so well. After a long series
of tests the same firm adopted 27I degrees for the spiral. This
angle makes the spiral groove of all drills start at the point with a
pitch equal to six diameters of the blank, the increase in twist being
a constant function of the angular movement of rotation of the drill
blank. This angle is based on holes from one to three diameters
deep. For deeper holes a smaller angle might be advisable and
greater angle for holes of less depth. There is practically no differ-
ence in torsional stress with the angle between 25 and 30 degrees.
SI
52
TWIST DRILLS
Sharpening Drills
Drills should be sharpened so as to cut the right size and with as
little power as possible. To cut the right size both lips must be the
same length and the same angle. A gage as shown in Fig, 4 will
help both to get the angle and to grind them central. This gives the
usual lip edge of 59 degrees. Fig. 5 shows how you can see if both
lips are ground alike, but does not give the angle. Fig. 6 is a sug-
gestion by Professor Sweet of relieving the drill back of the cutting
edge, making it similar to a flat drill in this respect.
For drilling brass or for any thin stock where the drill goes clear
through, it is best to grind the cutting edge parallel with the axis of
FIG. 9
FIG. 6
Grinding Twist Drills
the drill. This does away with the tendency to draw into the work.
Fig. 7 shows how this is done.
It is sometimes necessary to thin the point of the drill to get best
results. This requires care in grinding but can be done as shown
in Fig. 8.
The best all-around clearance angle is 12 degrees, though for
softer metals 15 degrees can be used. The 12 degrees is the angle
at the cutting edge, but this should increase back of the cutting edge
so that the line across the web should be 45 degrees, with the cutting
edges. This is important, as it not only saves power but prevents
splitting in hard service. The point of the drill should look like
Fig. 7 or Fig. 8. Fig. 9 shows the clearance angle and the right
angles for the drill point.
SPEEDS AND FEEDS
S3
Speed of Drills
Learn to run drills at their proper speed to secure the most work
with fewest grindings and breakages. The best practise is to use a
speed that will give 30 feet a minute cutting speed for steel, 35 feet
for cast iron and 60 feet for brass. This means that the cutting edge
must run fast enough to make these speeds. For drilling steel with
a xV-inch drill this means 1834 revolutions a minute, while for brass
it would be 3668 revolutions. The table gives the speeds without
any figuring for all drills up to 3- inches. These speeds require
plenty of lubricant. This is for carbon steel drills.
These speeds can be exceeded in many cases even with carbon drills,
and can be doubled with high speed drills, in fact from 75 to 150 feet
is not uncommon with 200 feet a possibility under good conditions.
The feeds in the table below can also be doubled in many cases.
Table of Drill Feeds
7=i
Inches of Feed per Minute at Cutting Speed of
2
"0
30 Feet-Steel
35 Feet-Iron
60 Feet-Brass
E
Q
Rev. per
Alinute
Feed .004-
.007
Rev. per
JNIinute
.004-.007
Rev. per
Minute
.004-.007
per Revolution
T^^
1834
7-33
12.83
2140
8.56
14.97
3668
14.66
25.76
i
917
3.66
6.41
1070
4.28
7^49
1834
7^33
12.83
1%
611
2.44
4.27
713
2.85
4.99
1222
4.88
8.58
i
458
367
1.83
3.20
535
2.14
3^74
917
3.66
6.44
Feed .007
.015
.007
.015
.007
.015
T%
2-57
5-5
428
S
6.42
733
5-14
II
1
S06
2.14
4.6
357
2.5
5^35
611
4.28
9.2
t\
262
1.83
3-9
306
2.14
4^58
524
3.66
7^8
h
229
1.60
3-43
268
1.87
4-
459
3.20
6.86
*
184
1.28
2-75
214
1.50
3.21
367
2.57
5-5
f
153
1.07
2.3
178
1.25
2.67
306
2.14
4.6
i
131
.91
1-95
153
1.07
2.29
262
1.88
3-93
I
115
.80
1. 71
134
.93
2
229
1.60
3-43
I^
102
•71
i-';3
119
•83
1.79
204
1-43
3.06
li
91.8
.64
1-37
107
•75
1.61
183
1.28
2.7s
if
83.3
•58
1.25
97.2
.68
1-45
167
1. 17
2.51
li
76.3
•53
I-I5
89.2
.62
1^38
153
1.07
2.3
I^
70-5
.49
1. 05
82.2
.57
1.23
141
•99
2. IT
I^
65-5
.45
•97
76.4
.53
I-I5
131
•94
1.90
I^
61. 1
.42
.92
71-3
•50
1.07
122
•85
I.81
2
57-3
.40
.85
66.9
.46
I.
115
.80
1-73
2\
51
.36
•71
59-4
.41
•89
102
•71
1-53
2h
4S.8
•32
.68
53-5
•37
.80
91.7
.64
1-37
n
41.7
.29
.62
48.6
•34
•73
83.4
•58
1. 21
3
38.2
.27
•57
44.6
•31
•^1
7^-4
•53 i^i5
54
TWIST DRILLS
Feed of Drills
The feed of drills is usually given in parts of an inch per revolution,
0.004 to 0.007 irich for drills of J inch and smaller and 0.007 to 0.015
inch for larger drills being recommended. This has been worked
out into the table for the standard speeds to show inches of feed per
minute for the three speeds given, which is more convenient. This
is not an iron-clad rule but should be used with judgment. For
high-speed steel these figures can be just about doubled.
Data for Drilling Cast Iron at Feed of \" per Min.
H.P. for
H.P. for
Size of
Feed per
Thrust in
I Inch
Size of
Feed per
Thrust in
I Inch
Drill
Rev.
Lbs.
Feed per
Min.
Drill
Rev.
Lbs.
Feed per
Min.
I
.02
1300
•0035
.06
8000
.02
.04
2600
.0063
2h
.02
3200
.008
.06
3900
.010
.04
6500
.016
li
.02
2000
.005
.06
9700
.024
.04
3900
.010
3
.02
3750
.009
.06
5800
.015
.04
7700
.019
2
.02
.04
2500
5300
.006
.013
.06
1 1 500
.029
For carbon steel the values run from i Ho 3 times these for cast
iron, increasing with the feed per revolution.
One inch flat twisted drills have been run from 313 to 575 r. p. m.,
with feeds of 11.27 and 28.1 inches per minute and required from 5.22
to 11.60 actual horse power.
Torque Required to Drill Cast Iron
Diam. of
Feed in
Inch
per Rev.
Pounds
Torque
at I foot
Radius
H.P. per
Diam of
Feed in
Inch
per Rev.
Pounds
Torque
H.P. per
DriU
Rev.
Drill
at I foot
Radius
Rev.
I
.02
50
.009
.06
390
.072
.04
80
.014
A
.02
200
.038
.06
120
.023
.04
400
.076
i^
.02
75
.014
.06
600
.114
.04
150
.028
3
.02
280
•053
.06
225
.042
.04
575
.109
2
.02
.04
125
25s
.023
.048
.06
870
.167
DRILL POINTERS $5
Drill Troubles
Twist-drills will stand more strain in proportion to their size and
weight than almost any other tool, and when a good drill gives trouble
it is pretty safe to say some of the conditions are wrong.
If it chips on the edge, the lip clearance is too great and fails to
support the cutting edge or the feed is too heavy. Ease off on the
feed first and then watch the grinding.
If it splits in the web it is either ground wrong, i.e., does not have
the center lip at the angle of 45 degrees or the feed is altogether too
heavy.
If the outer corner wears, it shows that the speed is too great.
This is pardcularly noticeable on cast iron.
Drill Pointers
In most cases it is better to use high speeds almost to the point
where the drill corners commence to wear with a light feed than to
use slower speed and heavy feed.
This is specially true of drilling in automatic machines where the
holes are not more than twice as deep as the diameter where drills
are flooded vat\\ lard oil. With deeper holes the chips are harder to
get rid of and it is better to use slower speeds and heavier feeds as
the drilled hole gets deeper. Speeds of 10,000 r, p. m. for drills i^in.
and smaller are not uncommon.
Watch the drill chip and try to grind so that it will come out in a
small compact roll. It is better to have this continuous clear to
bottom of hole if possible.
In drilling brass use a heavier feed especially on automatic ma-
chines, as it helps to work out the chips. If you lubricate at aU,
flood the work. Twist-drills ground as for steel often catch and
"hog in" on brass, especially at the bottom of the hole, where it
breaks through. To avoid this, grind the lead or rake from the
cutting edge.
In drilhng hard material use turpentine as a lubricant.
Drills feed easier by thinning the extreme point if this is carefully
done. This is important in hand feeding.
High-speed drills work best when warm. Lubricant should be
heated to 150 degrees F. when starting drills to work; they will soon
maintain the proper temperature.
Special Drills and Their Uses
Ratchet-drills have a square taper shank, are used in hand-ratchet
braces and in air-driven drills. Used in bridge building, structural
and repair work.
The shell drill, Fig. 10, is used after a two-groove drill in chucking
out cored holes or for enlarging holes that have been made with a
two-groove drill. It has a taper hole and a number of sizes can be
used on the same arbor.
56 TWIST DRILLS
Wire drills and jobbers or machinists drills both have round shanks
and only differ in size. Wire drills are made to a twist-drill gage and
the others to a jobbers or fractional gage.
Blacksmith drills all have a ^-inch shank 2j inches long, so as to
all fit the same holder. There is a flat on the shank for set-screw.
The straightway or Farmers drill has the same clearance as a
twist-drill but the flutes are straight. It is used mostly in drilling
brass and soft metals or in drilling cross holes or castings where blow
holes may be found, as it is less likely to run than the twist -drill.
Oil drills have the advantage of the cutting edge being kept cool
and of the chips being forced back through the grooves which reduces
friction to a minimum. They are used for all kinds of drilling,
mostly deep hole work. In cast-iron drilling air is sometimes used
to blow out the chips and keep the drill cool. They are generally
used in a screw or chucking machine or a lathe fitted for this work.
Where the drill is held stationary and the work revolves, the oil
is pumped to the connection and flows through the holes in the drill
as in Fig. ii.
Where the drill revolves
as in a drill press, the oil
is pumped into a collar
which remains stationary
while the drill socket re-
volves, as in Fig. 12. An
oil groove around the
socket and holes through
to the drill connects with
the holes in the drill it-
self. Other types are
shown in Figs. 13 and 14. Fig. 10. ■ — Shell Drill
The latter is used mostly
in screw or chucking machine turrets where the oil is pumped into
the center of the turret and into the large hole in the shank of the drill.
The hollow drill shown in Fig. 15 is used for deep drilling or long
holes and is used in a lathe or some similar machine fitted for the
purpose. It has a hole lengthwise through the shank connecting
with the grooves of the drill. The shank can be threaded and fitted
to a metal tube of such length as desired. The outside of the drill
has a groove the whole length of the body. The lubricant is con-
veyed to the point of the drill on the outside through these grooves,
while the hollow tube admits of the passage of oil and chips from
the point. In using this drill the hole is first started with a short
drill the size of the hole desired and drilled to a depth equal to the
length of the body of the hollow drill to be used. The body of the
hollow drill acts as a packing, compelling the oil to follow the grooves
and the chips to flow out through the hollow shank.
Three and four groove drills are used for chucking out cored holes
or enlarged holes that are first drilled with a two-groove drill. They
are much better than a two-groove drill for use in cored holes or to
follow another drill. The ends of the drills, Fig. 16 and 17, indicate
that they are not made to drill from solid stock but for enlarging a
hole already made-
TYPES OF DRILLS
57
Q
cn^B
FIG. II
FIG. 12
FIG. 13
FIG. 14
FIG. 15
FIG. 16
Q
FIG. 17
58
TWIST DRILLS
The following tables give standard drill sizes in various ways, each
being very convenient for certain classes of work:
Decimal Equivalents of Nominal Sizes of Drills
'*:'
i .
u
0 _
m
0
w
"o
tc
mJ^
M
tr.J^
£0
U3^
a
-- u
rt
0
i^
0
1^
0
1-
1
S
^
<,
^
a
^
J3
'0 ^
80
•0135
1.2
.047244
37
,104
79
.0145
1-3
.051181
2.7
.1063
i^
,015625
55
.052
2,(>
.1065
.4
.01574
54
.055 ^
-e\
.109375
78
.016
1.4
.055118
35
.11
77
.018
1-5
.05905
2.8
.11024
•5
,01968
53
•0595
34
.III
76
.020
r^.
.0625
33
.113
75
.021
1.6
.06299
2.9
.11417
74
.0225
52
•0635
32
.116
.6
.02362
1-7
.066929
3
.II8II
73
.024
51
.067
31
.12
72
.025
50
.07
3^1
.12205
71
.026
1.8
.070866
\
.125
.7
.02756
49
•073
3-2
.12598
70
.028
1.9
.0748
30
.1285
69
.02925
48
.076
3-3
.12992
68
.031
e\
.078125
3-4
.13386
■s\
•03125
47
.0785
29
.136
.8
.031496
2
.07874
3-5
.1378
67
.032
46
.081
28
.1405
66
.033
45
.082
^\
.140625
65
.035
2.1
.082677
3^6
.14173
•9
.03543
44
.086
27
.144
64
.036
2.2
.086614
3-7
.14567
63
.037
43
.089
26
.147
62
.038
2-3
•09055
25
•1495
61
.039
42
.0935
3-8
.14961
I
.03937
-h
'O9375
24
.152
60
.04
2.4
.09448
3-9
.15354
59
.041
41
.096
23
.154
58
.042
40
.098
z\
.15625
57
.043
2.5
.098425
22
.157
I.I
.043307
39
•0995
4
.15748
56
.0465
38
,1015
21
•159
e\
.046875
2.6
.102362
20
.161
SIZES OF DRILLS 59
Decimal Equivalents of Nominal Sizes of Drills, Continued
«
•0
ej
"0
^
•o
M
tn-£3
N
t«-d
N
,/i jd
0
1^
-in
U
|l
Q
^
1
■•gl
a
s
^
V
3
"0 0
Q
4.1
.16142
A
.234
p
•323
4.2
•16536
M
•234375
H
.328125
19
.166
6
.23622
Q
•332
4-3
.16929
B
.238
8.5
•33465
18
.1695
6.1
.24015
8.6
•33859
l\
•171875
C
.242
R
•339
17
•173
6.2
.2441
M
•34375
4.4
•17323
D
.246
8.8
.34646
16
.177
6.3
.24803
S
.348
4.5
.17717
i-
E
•25
9
•35433
15
.18
6.4
.25197
T
•358
4.6
.1811
6.5
•25591
If
•359375
14
.182
F
•257
9.2
.36221
13
.185
6.6
.25984
U
.368
4-7
.18504
G
.261
9^5
.37402
T%
•1875
6.7
.26377
1
•375
4.8
.18898
H
.265625
V
•377
12
.189
H
.266
9.6
•37796
II
.191
6.8
.26772
9.8
•38583
4.9
.19291
6.9
.27165
w
•386
10
•1935
I
.272
If
.390625
9
.196
7
•27559
10
•3937
5
.19685
J
.277
X
•397
8
.199
7^1
.27952
Y
•404
5.1
.20079
K
.281
M
.40625
7
.201
3^2
.28125
Z
■413
if
.203125
7.2
•28347
10.5
•4134
6
.204
7-3
.2874
II
•421875
5-2
.20473
L
•29
11
•43307
5
•2055
7-4
•29133
tV
•4375
5-3
.20866
M
•295 ^
"•5
•45276
4
.209
7^5
.29528
II
•453125
5-4
.2126
M
.296875
M
•46875
3
.213
7.6
.29922
12
.47244
5-5
.21654
N
.302
fi
•484375
z\
.21875
7^7
•30314
12.5
.4921
5-6
2
.22047
.221
7.8
7^9
.30709
.31102
i
•5
5-7
I
.22441
.228
A
8.
•3125
.31496
5-8
.22835
0
.316
5-9
.23228
8.2
.32284
6o TWIST DRILLS
Decimal Equivalents of Nominal Sizes of Drills, Continued
1^
0
05 -fl
rt a
2 fl
rt a
E^
E^
-d
s
•g^
^
s
"C c
-s
s
0 c
^'
Q
^
Q
^
Q
13
.51181
n
.671875
n
.84375
ff
.515625
H
.6875
21-5
.84646
if
.53125
17-5
.689
M
•85937s
13-5
.5315
i^
.703125
22
.86614
f*
.546875
18
.70866
i
.875
14
•55118
M
.71875
22.5
•88583
T%
.5625
18.5
.72835
n
.890625
14-5
.57087
n
.734375
23
.90551
n
.578125
19
.74803
^
.90625
15
.59055
f
.75 .
H
.921875
F
.59375
n
.765625
23-5
.9252
M
•609375
19-5
.76772
It
•9375
15-5
.61024
B
.78125
24
.94488
t
.625
20
.7874
U
.953125
16
.62992
H
.796875
24-5
.9646
U
.640625
20.5
.8071
U
.96875
16.5
.6496
n
.8125
25
•98425
u
.65625
21
.82677
n
.984375
17
.66929
n
.828125
I
I.
Letter Sizes of Drills
Diameter
Decimals
Diameter
Decimals
Inches
of I Inch
Inches
of I Inch
A H
.234
N
.302
B
. .238
0 A
.316
C
.242
P Ik
•323
D
.246
Q
•332
E i
•250
RM
•339
F
.257
s
•348
G
.261
Tff
.358
H il
.266
U
.368
I
.272
Vf
.377
■
•277
Wfl
.386
K j\
.281
X
.397
L
.290
YM
.404
Mil
.295
z
.413
SIZES OF DRILLS
6i
Decimal Equivalents of Drill Sizes from ^ to No. 8o
Size
Decimal
Size
Decimal
Size
Decimal
Equivalent
Equivalent
Equivalent
3^1
0.500
3
0.213
iV
0.0937
0.4843
4
0.209
42
0.0935
it
0.4687
5
0.2055
43
0.089
If
0.4531
6
0.204
44
0.086
t\
0-4375
if
0.2031
45
0.082
n
0.4218
7
0.201
46
0.081
z
0.413
8
0.199
47
0.0785
M
0.4062
9
0.196
/t
0.0781
Y
0.404
10
0.1935
48
0.076
X
0-397
II
O.191
49
0.073
If
0.3906
12
0.189
50
0.070
W
0.386
t\
0.1875
51
0.067
V
0.377
13
0.185
52
0.0635
1
0.375
14
0.182
tV
0.0625
u
0.368
15
0.180
53
0.0595
If
0.3593
16
0.177
54
0.055
T
0.358
17
0.173
55
0.052
s
0.348
ii
O.1718
e\
0.0468
#
0.3437
18
0.1695
56
0.0465
R
0.339
19
0.166
57
0.043
Q
0.332
20
O.161
58
0.042
H
0.3281
21
0.159
59
0.041
p
0.323
22
0.157
60
0.040
o
0.316
A
0.1562
61
0.039
A
0.3125
23
0.154
62
0.038
N
0.302
24
0.152
63
0.037
if
0.2968
25
0.1495
64
0.036
M
0.295
26
0.147
65
0.035
L
0.290
27
0.144
66
0.033
i\
0.2812
e\
0.1406
s\
0.0312
K
0.281
28
0.1405
67
0.032
J
0.277
29
. 0.136
68
0.031
I
0.272
30
0.1285
69
0.029
H
0.266
i
0.125
70
0.028
if
0.2656
31
0.120
71
0.026
G
0.261
32
O.I 16
72
0.025
F
0.257
33
O.I 13
73
0.024
E-i
0.250
34
O.I II
74
0.0225
D
0.246
35
O.IIO
75
0.021
C
0.242
6^
0.1093
76
0.020
B
0.238
36
0.1065
77
0.018
if
0.2343
37
0.104
sV
0.0156
A
0.234
38
O.IOI5
78
0.016
I
0.228
39
0.0995
79
0.0145
2
0.221
40
0.098
80
0.0135
3^
0.2187
41
0.096
62
TWIST DRILLS
TAP DRILL SIZES FOR REGULAR THREADS
These sizes give an allowance above the bottom of thread on
sizes j%- to 2; varying respectively as follows: for "V" threads,
.010 to .055 inch; for U. S. S. and Whitworth threads, .005 to .027
inch. These are found by adding to the size at bottom of thread, j
of the pitch for "V" threads, and | of the pitch for U. S. S. and Whit-
worth, the pitch being equal to i inch divided by the number of threads
per inch. In practice it is better to use a larger drill if the exact size
called for cannot be had.
Size
Tap
5!
Size of Drill
Size
Tap
i|
Size of Drills
u. s. s.
V
w
U. S. S.
V
W
1
1
•i
24
20
18
16
14
13
11
II
II
10
10
9
.138
.191
.248
.302
.354
.409
.402
.465
.518
.581
.632
.695
• 745
.III
.184
.239
• 293
•345
•399
•391
■453
.506
• 568
.618
.680
.728
.129
.192
.249
.303
•355
.410
•403
.466
.520
.583
• 634
•697
•747
if
2''
9
8
8
7
7
6
6
5^
5
5
li
.808
•854
•917
1.082
1. 179
1.304
1. 412
1.390
I.5I5
1.640
1. 614
1-739
• 790
.832
.894
•932
I-OS7
1. 144
1.269
1.372
1-347
1.472
1^597
1.566
1.691
.810
.856
.919
.960
1-085
1. 182
1.307
1. 416
1-394
I-5I9
1.644
1. 619
1.744
A very simple rule, wliich is good enough in many cases, is:
Subtract the pitch of one thread from the diameter of the tap.
A f-inch tap 16- thread would be | minus jV = re drill; a f-inch
tap, ten-thread, would be f minus i^ = yVo — t\Po or 0.75 — o.io =
xVo or 0.65, or a little over f of an inch, so a f-inch drill will do
nicely. With a i-inch tap we have i — | = |-inch drill, which is a
little large but leaves enough thread for most cases.
Tap Drills
FOR S. A. E
. (A. L. A
. M.) Threads
Size of
Threads
Size of Drill,
Size of
Threads
Size of Drill,
Tap
per Inch
Inches
Tap
per Inch
Inches
1
28
7
a
16
*a
i^
24
Vz
1
14
§§
f
24
n
14
II
/s
20
f
12
leV
h
20
1^^
12
U\
I
18
12
in
f
18
If
12
in
ih
16
11
The tap should be between 0.002 and 0.003 inch large for clearance
between top and bottom of threads.
TAP DRILLS
63
TAP DRILLS
For Machine Screw Taps
These drills will give a thread full enough for all practical purposes
but not a. full thread as this is very seldom required in practical work,
Further data along this line will be found in the tables which follow.
Tap Drills
Sizes of
No. of
Sizes of
Sizes of
No. of
Sizes of
Taps
Threads
Drills
Taps
Threads
Drills
2
48
48
12
24
19
2
56
46
13
■^O
17
2
64
45
13
24
15
3
40
48
14
20
14
3
48
47
14
22
13
3
56
45
14
24
II
4
32
45
15
18
12
4
36
43
15
20
10
4
40
42
15
24
7
5
30
41
16
16
10
5
32
40
16
18
7
5
36
38
16
20
5
5
40
36
16
24
I
6
30
39
17
16
7
6
32
37
17
18
4
6
36
3S
17
20
2
6
40
33
18
16
2
7
28
32
18
18
I
7
30
31
18
20
B
7
32
30
19
16
C
8
24
31
19
18
D
8
30
30
19
20
E
8
32
29
20
16
E
9
24
29
20
18
E
9
28
27
20
20
F
9
30
26
22
16
H
9
32
24
22
18
I
10
24
26
24
14
K
10
28
24
24
16
L
10
30
23
24
18
M
10
32
21
26
14
0
II
24
20
26
16
P
II
28
19
28
14
R
II
30
18
28
16
S
12
20
21
30
14
T
12
22
19
30
16
U
64
TWIST DRILLS
Dimensions for Twist Drills
for boring holes to be threaded with u. s. form of thread
TAPS jV to il INCH DIAMETER
Diam-
No. of
Threads
to the
Inch
Exact
Diameter
Gage
Diam-
No. of T^?
Threads ^\
to the ^9^
Inch {
.xact
ameter
Gage
eter
Bottom of
No. of
eter
tom of
No. of
Inches
Thread
Inches
DriU
Inches
hread
nches
DriU
tV
6o
.041
57
1
4
26
200
6
T>
64
.042
56
^T
56
055
53
•5" 2
48
.067
50
WV
60
056
53
A
50
.068
50
-^'^
40
077
46
A
56
.071
49
^'^
44
080
45
A
60
.072
48
^^
48
082
44
i
40
•093
41
6\
32
100
38
i
44
.096
40
/.
36
105
36
i
48
.098
39
6^T
40
108
34
^
32
.116
31
U
32
131
29
^
36
.120
31
U
36
136
28
3^2
40
.124
30
U
40
139
28
24
•133
29
u
24
149
24
28
.141
27
u
28
157
21
tV
30
.144
26
H
32
162
10
tV
32
.147
25
H
36
167
18
tV
36
.152
23
24
I So
13
T^^W
24
.164
19
il
28
188
10
^V
28
.172
16
61
32
194
8
j'^
32
.178
14
i^
36
ig8
7
-h
36
.183
12
iT
18
193
9
i
18
.178
14
^-4
20
201
5
i
20
.185
12
h
24
211
3
i
22
.190
10
h
26
216
2
i
24
.196
8
n
32
225
I
Drills and Reamers for Dowel Pins
Sizes of Rod
Drills and
Reamers for
Drive Fits
Drills for
Clearance
No. of Gage
(Stubbs Steel
Wire)
Dia.
Size of
Dia. of
Dia. of
Size of
Dia. of
Drill
Drill
Reamer
Drill
Drill
54
.OSS
No. 55
.052
No. 54
•055
45
.081
" 47
.0785
" 46
.081
33
.112
" 36
.1065
.110
" 33
•"^
30
.127
31
.120
.125
" 30
.1285
21
.157
" 24
.152
•155
22
•157
10
.191
" 13
.185
.189
" II
.191
.2S2
c
.242
.250 -.2505
F
.257
•315
■is Reamer
Drill
.307
■3r25-.3i3
0
.316
V
.377
1
'
.366
■375 --3755
V
•377
.439
^s
'
.427
•4375--438
• SO 3
^
'
.489
.500 -.5005
.628
1
.616
.625 -.6255
.753
1 *
.734(11)
.750 -.7505
TAP DRILLS
Double Depth of Threads
65
Threads
V
Threads
U.S.
St'd
Whit.
St'd
Threads
V
Threads
U.S.
St'd
Whit.
St'd
per in.
DD
DD
D D
per in.
DD
DD
DD
2
.86650
.64950
.64000
28
.06185
.04639
.04571
2i
.77022
•57733
.56888
30
.05773
.04330
.04266
2f
.72960
.54694
.53894
32
.05412
•04059
.04000
2h
.69320
.51960
.51200
34
.05097
.03820
.03764
2f
.66015
•49485
.48761
36
.04811
.03608
.03555
2f
.63019
.47236
•46545
38
.04560
.03418
.03368
2I
.60278
.45182
.44521
40
.04330
.03247
.03200
3
.57733
.43300
.42666
42
.04126
.03093
.03047
3i
.53323
.39966
.39384
44
.03936
.02952
.03136
3h
.49485
.37114
.36571
46
.03767
.02823
.02782
4
.43300
.32475
.32000
48
.03608
.02706
.02666
4l
.38488
.28869
.28444
50
.03464
,02598
.02560
5
.34660
.25980
.25600
52
.03332
.02498
.02461
5i
.31490
.23618
.23272
54
.03209
,02405
.02370
6
.28866
.21650
.21333
56
.03093
02319
.02285
7
.24742
.18557
.18285
58
.02987
.02239
.02206
8
.21650
.16237
.16000
60
.02887
.02165
.02133
9
.19244
.14433
,14222
62
.02795
.02095
.02064
10
.17320
.12990
. 1 2800
64
.02706
.02029
.02000
II
.15745
.11809
.11636
66
.02625
.01968
.01939
11^
.15069
.11295
.11121
68
.02548
.01910
.01882
12
.14433
.10S25
.10666
70
.02475
.01855
.01828
13
•13323
.09992
.09846
72
.02407
.01804
.01782
14
.12357
.09278
.09142
74
.02341
.01752
.01729
15
.11555
.08660
•08533
76
,02280
.01714
.01673
16
.10825
.08118
.08000
78
.02221
.01665
,01641
18
.09622
.07216
.07111
80
.02166
.01623
.01600
20
.08660
.06495
.06400
82
.02113
.01584
.01560
22
,07872
•05904
.05818
84
.02063
.01546
.01523
24
.07216
.05412
•05333
86
.02015
.01510
.01476
26
.0661
.04996
.04923
88
.01957
.01476
.01454
27
.06418
.04811
.04740
90
.01925
.01443
.01422
This gives the depth to allow for a full thread in a nut or similar
piece of work for threads for 2 to 90 per inch, regardless of the diam-
eter. A special nut for a 2-inch bolt, 20 threads per inch, U. S,
Standard would have a hole 2. — .06495 = 1.93505 inches in diam-
eter bored in it.
66
TWIST DRILLS
Sizes of Tap Drills for Taps with "V" Thread
1
1
I
K
s"
a
■^
H-S
P^
^-s
Q
H-g
Q «
h|
Q s^
1l
^1
•i5
•^
l-s
-ol
l-s
^■s
g.c
^^
?^2
1^
§^
rt.S
^^
I.S
l^g
§^^
S
H
Cfi
Q
H
w
5'"
H
•(n
Q
H
w
^
48
50
3^
24
No. 20
if
12
fi
lA
7
lei
3^^
52
50
¥
28
No. 17
it
14
i
lA
8
I6\
^\
54
49
^^
30
No. 16
f
10
M
li
7
I.\
?\
56
49
3V
32
No. 15
i
II
h
lA
7
lA
A
60
48
if
24
No. 16
1
12
If
ifV
7
I^T
^?
32
50
il
2S
No. 1 2
fi
10
If
lii
7
lA
^?
36
49
if
32
No. 10
li
II
il
If
6
li
40
47
i
18
No. 17
M
12
If
lif
6
1/2
"&%
48
44
i
20
No. 14
;i
II
T^.
i-V
6
lA
eV
56
43
i
24
No. 9
12
If
I-f
6
1/2
i
32
44
3^
16
No. 10
If
II
if
6
li:
i
3(>
43
3%
18
if in.
If
12
II
1^1
6
l\:
i
40
42
3\
20
No. 3
f
10
II
IT^6
6
l|
i
42
41
A
16
No. I
f
II
A
lit
6
I|^
1
48
39
18
if in.
f
12
if
5
i|f
^\
30
41
ii
16
F
ft
10
64
if
5i
i|f
is\
32
40
i\
18
il in.
If
II
|-
^W
5
I|^
^\
36
37
t
14
J
If
12
¥¥
5i
i|t
A
40
34
f
16
L
il
ID
It
ifi
5
i|^
-,%
30
33
1
18
il in.
¥
10
f-
iH
5i
i|t
3\
32
32
if
14
N
9
If
iff
5
III
A
36
31
if
16
P
1
10
II
i|f
5^
III
40
30
if
18
If in.
9
1
If
5
III
32
30
j'g
14
R
il
9
-f
i|f
5
i|f
ri
36
29
tV
16
S
-^
9
-f
Iff
5
i|f
■ji
40
28
if
14
f in.
8
-;j
ill'
5
i|f
A
24
29
15
32
16
W
I3V
8
li
4i
i|f
A
28
28
i
12
if in.
II^
8
-^^
li
5
III
A
30
27
i
13
X
lA
8
If
III
4i
Iff
3
T6
32
26
i
14
if in.
7
II
isf
5
36
24
il
12
It in.
i\
8
If
I- 6
4i
iff
il
24
26
il
13
II in.
lA
7
It
I-l
5
iff
if
28
22
il
14
tV in.
lA
8
I-l
4i
iff
if
32
20
A
12
II in.
lA
7
If
I-i
5
Iff
if
36
18
rV
14
if in.
lA
8
leV
2
4i
Iff
This table gives similar information but in a way that would be
more convenient in some cases.
TAPPING AND THREADING 67
TAPPING AND THREADING SPEEDS
For tapping in cast iron, the F. E. Wells & Son Company, Green-
field, Mass., recommends the following speeds:
f inch holes
382 255 191 153 127
using an oil or soda compound.
For soft steel and iron:
i f i f I inch holes
229 153 115 91 76
using oil as a lubricant.
The National Machine Company, Hartford, Conn., uses 233 revo-
lutions per minute up to J inch diameter and 140 revolutions per
minute for sizes between | and ^ inch, using a screw-cutting oil as
a lubricant.
They tap holes as deep as four tap diameters by power.
For threading cast iron in machines of the bolt-cutter type, the
Landis Machine Company, Waynesboro, Penn., gives these speeds:
i f h f I I2 2 inches
200 150 125 100 85 55 45
with petroleum as a lubricant.
For soft steel and iron :
i f h f I i| 2 inches
280 220 175 140 115 75 60
with compound or screw-cutting oil, using a 2^-inch belt at 1200 feet
per minute. The speeds are for high-speed steel dies. Some users
run the machines at a much higher rate.
Threading Pipe
The Bignall & Keeler Manufacturing Company, Edwardsville,
111., aims to have its pipe-threading machines run at a cutting speed
of 15 feet per minute. The machine for handling pipe from I to 2
inches uses a 3|-inch belt at about 940 feet per minute. They advise
nothing but lard oil on the dies.
The Standard Engineering Company, Ell wood City, Penn., also
recommends a cutting speed of 15 feet per minute, using a 3-inch
belt at 730 feet per minute.
It will be understood in all the cases cited that the figures given
are merely a guide as to what can be done and not record perform-
ances in any particular. Soft stock can be run very fast, and hard,
gritty stock is very hard on the dies.
The only general rule, in the case of dies, is to run as fast as possible
without undue heating of the dies.
68
TWIST DRILLS
DRILL END LENGTHS
It is often necessary in designing brass castings to allow for drilling
to a certain depth so as to give the thickness of metal A necessary
at the bottom of the hole to withstand pressure.
The table gives the dimension C for usual sizes of drills. This
is deducted from B to give the actual thickness of metal at A .
Drill End Lengths
Cin
Gage
Cin
Gage
Cin
Dia.
c
near-
est ,\
No.
Dia.
c
near-
est ,h
No.
Dia.
C
near-
est o'4
2
0.60086
If
I
0.2280
0.06850
0^5
41
0.0960
0.02884
T?2
^"4
0.58208
64
2
0.2210
0.06640
C^
42
0.0935
0.02809
3^2
li
0.56331
A-
3
0.2130
0.06400
A
43
0.0890
0.02674
^^
^^1
0-54453
^1
4
0.2090
0.06279
iV
44
0.0860
0.02584
^z
If
0.52576
u
0.2055
0.06174
IV
45
0.0820
0.02464
3*2
li^
0.50698
1
6
0.2040
0.06129
A-
46
0.0810
0.02433
If
0.48820
u
7
0.2010
0.06039
IV
47
0.0785
0.02358
^¥
0.46942
Vi
8
0.1990
0.05979
I^.
48
0.0760
0.02283
s
'^
0.45065
n
9
0.1960
0.05888
I^I
49
0.0730
0.02193
^
'<«
0.43187
/•T
' 10
0.1935
0.05813
^,
50
0.0700
0.02103
aV
If
0.41309
hi
II
0.1910
0.05738
IV-
SI
0.0670
0.02013
3»2
lA
0.39431
n
12
0.1890
0.05678
1^6-
52
0.0635
0.01908
e^S
li
0.37SS4
i
13
0.1850
0.05558
^,
53
0.0595
0.01788
h
^j\
0.35676
n
14
0.1820
0.05468
A-
54
0.0550
0.01652
~h
li
0.33798
a
15
0.1800
0.05408
^s
55
0.0520
0.01562
B^
iiV
0.31931
fi
16
0.1770
0.05318
^e
56
0.0465
0.01397
e^
I
0.30046
u
17
0.1730
0.05197
^e
57
0.0430
0.01292
6\
il
0.29104
i'i
18
0.1695
0.05092
#
58
0.0420
0.01262
B^
il
0.28165
^%
19
0.1660
0.04987
59
0.0410
0.01232
M
0.27226
A
20
0.1610
0.04837
s\
60
0.0400
0.01202
V
i
0.26288
11
21
0.1590
0.04777
6^
61
0.03Q0
0.01172
B4
\'i
0. 25349
"i
22
0.1570
0.04717
,\
62
0.03S0
0.01142
&i
• 8
0.24410
i
23
0.1540
0.04627
#
63
0.0370
0.01112
¥
0.23471
V
24
0.1520
0.04567
64
0.0360
0.01082
B4
f
0.22532
T?J
25
0.149s
0.04491
b'?
6S
0.0350
0.01052
h
u
0.21593
5^2
26
0.1470
0.04416
e%
66
0.0330
0.00991
6^
u
0.20655
li
27
0.1440
0.04326
6^3
67
0.0320
0.00961
u
0.19716
U
28
0.1405
0.04221
B^i
68
0.0310
0.00931
6^3
1
0.18777
A
29
0.1360
0.04086
#4
69
0.0293
0.00879
b\
M
0.17838
u-
30
0.1285
0.03861
#
70
0.0280
0.00841
B^S
T%
0.16900
n
31
0.1200
0.03605
71
0.0260
0.00781
b\
¥
0.15960
A
32
0.1160
0.03485
72
0.0250
0.00751
h
h
0.15022
{'■z
33
0.1130
0.03395
B"
73
0.0240
0.00721
h
¥
0.14083
¥
34
O.IIIO
0.03335
^.
74
0.0225
0.00676
b\
/,?
0.13144
1
35
0.1100
0.03305
^\
75
0.0210
0.00631
^
a
0.12205
1
36
0.1065
0.03200
^\
76
0.0200
0.00601
B^
t
0.11266
V
H
0.1040
0.03124
^\
77
0.0180
0.00541
B»4
u
0.10327
0^3
38
o.iois
0.03049
^
78
0.0160
0.00481
i^e
0.09388
#2
39
0.0995
0.02989
^
79
0.0145
0.00436
#
0.08450
3%
40
0.0980
0.02944
^,
80
0.0135
0.00406
i
0.07511
«\
Tf-
0.06572
1^0-
A-
t
0.05633
3
Fon
iiuIa,C=
0.60086 DUm.
0.04942
0.037SS
g
f^
^S
'^MM
0.02817
0.01878
0.00939
A
K
^^
\!//'
s
^P^
Wmi
MACHINE SCREW TAPS
69
^-^^
y .^-G-H
Dia. of Neck =Eoot Dia.
Dimensions of Machine Screw Taps
M
UH UH
0
°,.r^
M
0
0
0
^
ii
^
-T3 0
ja-Td
43 j3
t-l
Number of
Tap
111
i
3
s
II
(DC/3
6
Q
2
H
J
h:i K^l
Q
k1
C/2
:z;
A
B
C
D E
F
G
H
I
.071
64
i|
T%
g It
V
.125
t\
^\
3
li
.081
56
li
T%
T3 It
V
.125
^
3\
3
2
.089
5^
li
T^W
^ . It
V
.125
l'^
^^.
3
3
.101
48
i^
ft
"" g ^'
.125
t\
3\
3
4
•113
36
2
H
-^1 It
^w.
•125
r\
^
3
5
.125
36
2i
f
^ 1
.125
if
A
3
6
.141
32
2i
i
0 i|
.141
3^
eV
3
7
•154
32
2i
f
^ i|
•154
■^'7,
eV
3
8
.166
32
2i
if
i IT
^^
.166
/^
i
4
9
.180
30
2i
^
i I^
.180
1
4
i
4
10
.194
24
2i
1
i il
.194
i
^\
4
II
.206
24
2|
^
i I^
.206
i
3^«
4
12
.221
24
2f
H
t ^^
V
.221
^^2
<2
4
13
•234
22
2i
I
tV la
%
.234
-,%
t^w
4
14
.246
20
2ft
ItV
T^^ li
-
.246
j\
tV
4
15
.261
20
2|
li
T6 l3
-'«
.261
tV
T^«
4
16
.272
18
2f
I^
t\ II
-V
.272
fv
/^
4
18
.298
18
2f
li
t\ n
-V
.298
T^^
^v
4
20
.325
16
3
li
i i^
-
•325
M
i
4
22
•350
16
3
li
i il
-
.■7crc
ii
4
24
.378
16
3i
li
tV h
-*
.378
t
s%
4
26
.404
16
3i
li
t\ i^
6
.404
t
fV
4
28
.430
14
3i
I*
T^ I^
•430
it
T^^
4
30
.456
14
3i
If
T^6 I-
lI
.456
I'e
ii
4
These are for the American Screw Company's Standard screws
that have been in use for many years.
70
TAPS
Machine Screw Taps-
(Wells Bros. Co.)
Outside
Size
Threads
per Inch
Size
steel
Dia. Thread
Whole
Length
Length
Thread
Length
Square
Diara.
Max.
Min.
Square
A
B
C
D
E
o
80
147
.063
.061
lA
V
t72
.112
I
72
147
.076
.074
If
1^5
.112
2
64
147
.089
.088
i5l
l\
^5
.112
3
S6
147
.103
.101
isi
f
Tf5
.112
4
48
147
.116
.114
iVn
38-
3\
.112
5
44
147
.i2g
.127
m
\l
1^5
.112
6
40
147
.142
.140
2^,
\l
t75
.112
7
36
105
•155
•153
2^\
\
\
.124
8
36
174
.169
.167
2h
11
• 131
9
32
187
.181
.179
2A
\%
.140
lO
30
200
.194
.192
2il
\\
.150
II
215
.206
.204
2\
I
~i
.161
12
28
226
.220
.218
2A
I^-^
A
.170
13
252
•239
• 237
'?!
I^^
#
.189
14
24
252
.246
• 244
2\\
III
T?2
.189
15
258
.258
.256
2 f
li
?'^
•194
i6
22
278
■ 273
.270
23^
i|
'^%
.209
i8
20
304
.299
.296
2 1
I3\
A
.228
20
20
iil
■325
•322
2i3
lA-
/s
.249
22
18
370
366
•351
•348
2\
13^2
l"«
.278
24
16
387
383
•377
•374
2\l
13%
A
• 215
26
16
418
414
•403
.400
3
lA
^J
.236
28
14
449
445
•430
.427
35V
If
W
• 249
30
14
480
476
.456
•453
3i
I/.
u
.268
Pitch Dia.
Size
Pitch Dia.
•
Size
Pitch Dia.
Size
Max.
Mm.
Max.
Min.
Max.
Min.
0 X80
•0538
.0528
7 X36
• 1359
•1345
16 X22
.2421
2403
I X 72
.066
.065
7 X32
• 1337
•1323
16 X 20
.2394
2374
I X64
•06s
.064
7 X30
.1325
• 131
18 X 20
.2652
2634
2 X64
.078
.0769
8 X36
.1489
•1475
18 X 18
.2618
2598
2 X 56
.0767
.0756
8 X32
.1467
•1453
20 X 20
.2912
2894
3 X56
.0897
.0S86
8 X30
• 1454
.144
20 X 18
.2878
2858
3 X48
.0879
.0868
9 X32
.1598
.1583
22 X 18
•3138
3118
4 X48
.1010
.0998
9-X30
.1584
.1569
22 X16
•3094
3074
4 X40
.0984
.0972
9 X 24
• 1532
.1517
24X18
•3398
3378
4 X36
.0967
•0955
10 X 30
.1716
.170
24 X 16
.3354
3334
5 X44
.1129
.1116
10 X32
.1729
.1713
26 X 16
.3614
3594
5 X 40
.HIS
.1102
10 X 24
.166
.1647
26 X14
•3557
3537
5 X36
.1098
.1085
12 X 28
.1961
.1944
28 X 16
■^^o^
3854
6 X 40
.1246
.1232
12 X 24
• 1927
.1907
28 X 14
.3818
3797
6X36
.1229
•1215
14 X 24
.2184
.2167
30 X 16
•4154
4134
6X32
.1207
•II93
14 X20
.2134
.2114
30 X 14
.4077
4056
HAND TAPS
71
Dimensions op Hand Taps
(Wells Bros. Co.)
Small Shank Taps
U. S. S., Whit, and
all V Taps Incl.
aV over
Size
Pitch
Total
Length
Length
Length D
iam.
Diam.
Length
Thread
Shank
Square Sq
uare
Shank
A
B
C
D
E
F
i
20
2 ^
U
145
.%
134
• 173-175
i';,
18
2
iiV
I/.
TB
176
.228-230
1
16
2
^t
I f
f
217
.283-. 28s
<«
Ji,
3 5
I •
I f
M
254
■330-.332
1
St'd
3 f
I 1
T^T
286
•373--375
<«
12
3 f
2
§
321
•429
1
II
3i5
2l^,
41
359
479
iJ
II
4,
2i
41
406
542
1
10
4i
2
2\
li
442
590
i|
10
4i'.i
2i
2A
H
489
652
9
4ii
2i
2/ii
f
523
697
ii
9
4l
2|
2i
n
569
759
I
8
5i
2x^,1
2ii
600
800
1,^8
St'd
5i
2r^T
2}^
8
647
862
^^
7
5/.-
2f
2^
§3
672
896
14-
7
Si's
2}.\
2l
-3I
719
959
li
7
5iJ
2 f
2\%
I
766
I
021
'^:*
St'd
5ii
2}i?
3
Il^a
813
I
084
If
6
6
2j
3l
iiV
831
I
108
ii>
6
n
2iS
3/,^
li
878
I
170
li
6
6i
3
3i
Ij
925
I
233
lA
St'd
6/,
3^
3t
Il'g
971
I
296
If
St'd
6i«.
3l
3/b
lA-
978
I
305
"i^
St'd
M
3i\
3§
li
025
I
367
I f
S
61 3
3i
3t^,t
li
072
I
430
III
1 1
^ ?.
7
3A
3i^
lA
119
I
492
St'd
7 -
3l
3f
lA I
139
I
519
lii-
St'd
7i
3/,T
3Jg
If
186
I
582
2
4f
7t
M
3l
If
233
I
644
2-
c4*
7i?,
3l
4t^t
If I
327
I
769
2 i
St'd
7tl
3l
Az\
I/. I
421
I
894
2 -
St'd
8i
3l
Ai
i/b
514
2
019
2 ^
4
8^
4
Ah
l/e I
575
2
100
2-
4
su
4 f
A\}.
l| I
668
2
225
'f
St'd
9i'.^
4 4
A\l
li
762
2
350
2|
St'd
9l
4 -
5
11^6 I
856
2
475
3
3i
9f
4 3
5i
lA
906
2.542
72
TAPS
o
m
-G—
Wi
Regular Lengths over all
are 11, 12, 14 aiid 15 Inches.
Dimensions of Tapper Taps
^-d
?!
o
0
0 «
Diameter of
Number
f^
Diameter of
Diameter of
E
Tap
per
Inch
c
£5l
H-1
Shank E
Point F
"o
1
A
U.S.
V.
B
D
u s.
V.
US.
V.
St'd
St'd
Sfd
St'd
St'd
St'd
t
20
20
If
li
1
0.170
0.150
0.179
0.158
A
i8
i8
2
li
f
0,225
0.200J 0.234
0.210
f
i6
i5
2
li
f
0.280
0.250^0.287
0.261
^
14
14
2i
if
*
0-330
0.300^0.338
0.307
h
13
12
2i
If
1
0.3^5
0.3400.393
0.348
f^
12
12
2 +
't
0.440
0.400 0.446
0.41 1
f
II
II
2^
i^
O.dQO
0.4550.499
0.462
ii
II
II
2I
i^
0.555
0.515 0.561
0.523
A
lO
lO
2i
It
li
0.605
0.560 o.6ti
0.570
¥
lO
lO
2|
i|
If
0.670
0.625 0.673
0.631
i
9
9
3
If
0.720
0.675 0.722
0.675
if
9
9
3
li
0.780
0.7300.783
0.736
I
8
8
3i
2
0.820
0.770 0.828
0.775
i|
7
7
3^
2
0.925
0.860 0.928
0.869
li
7
7
3^
2
1.050
0.985 1.053
0.993
If
b
6
4
2f
I-I45
1.070 1. 147
1.075
• ih
5
6
4
2f
I*
1.270
1. 1951.272
1.200
Note. — Tapper taps differ from machine taps in not having a
square on the end of the shank. They are used in nut tapping
machines, the nuts being run over the tap on to the shank and when
full the tap is removed and the nuts slid off. The tap is then re-
placed for another lot of nuts.
PIPE TAPS
73
bo
1
o
■^^OOOCT. OrOrOO \O00»OM
1
o
NvOO^rO liOOOOOM 0<N0viO
ajnij
•^TJ-'trJ-Tt lOioOO OOOO
•spqx
WOOOO'*^ "mm'^mm COOOOOCO
1
.£2
Q
Ul
COtSMMf-. ^00<NO 00VOIJ--IO
(NfO^iovO OOOvH^a- voOvwiN
H->
MHMM CN<NOCO
K
o
fin
'
w
■"•n "h "2 ""n ^r? '*' "'"' '-*"' '^'' "'" '-''" "''^ "'"'
fi -""-"-= ~-„t rr-rr
u
nla> mgo -<IM m-< t-W -<K -i|« nl-« ^^^ <-::» ^li
pq
"Wi --5 -S "W "1" WW BM nw MM c^; «;«. 1^ m*
MHMM MMHM MN<NCI
t^OOOO-*'* MMMM 00000000
azjS
w w w N N to to t
i
74
TAPS
o
u
o
V
ii
(N
0^
On
t^
0
PO
H
M
ro
10
CO
0
'^
•
M
M
Q
■H«
.Hl-Jl
rHi-*
<
'^in
nloo
o
M
nloo
H2
M
H2
M
«loo
M
t-lM
r-IlM
i-l[M
to
m
rHl^
c,|«
H
m\m
H
M
<;
«|C0
1-1^
HN
rHlN
«|«
t-|0O
<N
<N
CN
<N
C^
^
l^
CO
CO
CO
C/3
CO
CO
C/2
^^
^^
^c/3
r^^
^c/^
^^
J?^
^^
8^
0^
8^
8^
0^
0^
0^
^rt
' 0
■ 00
■ 0
■ '^
w
' <N
■ 0
Pin
M
M
M
M
M
M
8i
^-
0
0
0
-*
ON
OO
0
LO
0
On
'^i-
P^Q
q
^
CN
-
s
.3
00
0
0
Tt
M
00
00
M
10
00
0
ro
00
i
M
M
<N
<N
CO
Q
J2
^
S
0
CN
<N
0
fO
0
0
>r
10
00
0
rO
Ch
"•
M
M
cs
<N
CO
(H
.9
uo
^O
0
r^
C)
t^
cs
V
0
0
■sO
10
5
S
I-;
(N
M
CO
CO
t^
00
IN
0
ro
0
10
CA
rt
<N
0
0
-O
LO
°
^
M
(N
CO
CO
«-^T3
t^
^
>o
C^
00
00
0
tJ-
t^
10
(N
t^
M
-
<N
<N
CO
CO
^1^-5
c
00
•^
<N
00
00
vO
52;^ aj
rO
M
M
M
o
0
rtloo
-^
-'^
-%
i-(|-*
'^
«|«)
TAPER DIE TAPS
75
k-F-
— B-
DJam. of Shauk Eopt Diam. less 0.015
Dimensions of Taper Die Taps
Diameter
Length
Length
Length
Total
Length
Size
Number
of
Tap
of
Shank
of
Thread
Straight
Thread
Length
of
Square
of
Square
of
Flutes
A
B
c
D
E
F
G
i
li
2
i
3i
T%
i
5
A
li
2-}
t\
4
i
iV
5
f
i^
3
*
4i
H
A
5
tV
If
3}
tV
5
H
i
5
h
2
3i
i
5^
f
3^^
5
A
2i
3f
T^IT
6
if
5
f
2^
4
ft
6i
if
11
5
H
2f
4i
H
7
^
M
6
i
3
4^
f
7^
1
tV
6
it
3i
4f
H
8
if
i
6
1
,S^
5
^
8J
I
i
6
if
3^
5i
H
8f
I
A
6
I
3i
5^
I
9
ItV
ft
6
li
3^
5i
ih
9i
ll
if
6
li
3^
6
li
9*
itV
f
7
If
3ft
6i
Ift
9f
lA
if
7
i^
3ft
6t
I*
lO
if
1 6
7
If
3f
6ft
Ift
loi
I 16
I
7
If
3ft
6J
If
loj
ih
II^^
8
i|
38
7*
I^
lof
if
li
8
2
3f
7f
2
II
lif
li
8
76
TAPS
h-H-^
Dimensions of Sellers Hobs
X
'o
o
"o o
Sf
0
s
6 o
.2K
Number of
Threads
per Inch
Diameter
of Pilot
B
HI
•5 "3
Ut-H
^^1
■3
Diameter
of Shank
G
0£
Q
hJ
h-1
h:i
H
^
CO
^
A
U.S.
St'd
V.
St'd
U.S.
St'd
V.
St'd
c
D
E
F
U.S.St'd
V. St'd
H
J
i
20
20
A
A
2
li
li
4i
0.170
0.150
f
i
6
T^«
i8
i8
tV
T^«
2
li
li
4i
0.225
0.200
f
■^'2
6
1
i6
i6
i
i
2i
ly'fi
ItV
•S
0.280
0.250
f
t\
6
V^
14
14
tV
i
2i
it\
lA
,si
0-330
0.300
H
i
6
i
13
12
t
tV
2i
iH
lit
s^
0.385
0.340
H
J%
8
t'w
12
12
t
f
2}
li
li
6
0.440
0.400
If
tV
8
^
II
11
i
t
2i
2i
2i
6i
0.490
0.455
i
8
ii
II
II
i
i
2i
2i
2^
7
0-55S
0.515
i
it
8
i
lO
lO
i
i
2i
2i
2i
7i
0.605
0.560
i
Tfi"
8
i*
lO
lO
i
i
2i
2f
2f
8
0.670
0.625
n
i
8
^
9
9
^i
i
2i
^
3
8i
0.715
0.675
H
i
8
i^
9
9
H
H
2i
■si
3i
9
0.780
0.730
I
9
Tfi
10
I
8
8
H
H
2ft
3i^6{3iV
9i
0.825
0.770
I
ft
10
li
7
7
i
Ti
2ft
3^3t^
9f
0.925
0.860
itV
H
10
li
7
7
8
i
2ft
3HI3H
10
1.050
0.9S5
ItV
i
10
ll
6
6
iiV
i
2ft
3l^i3it
loi
1. 145
1.070
li
H
10
li
6
6
itV
itV
2ft
4t'6I4T6
II
1.270
1.200
I^
H
10
I^
5^
5
lA
li
2f
4f
4t
iii
1-375
1.265
li
I
12
ll
5
5
IT^W
Ifv
2|
4ft
4t
12
1-475
1.390
li
itV
12
li
5
4i
li
IT%
2i
4i
4i
I2i
1.600
1-475
IT%
li
12
2
4i
4h
li
li
2f
5i
5i
13
1.700
1.600
if iii
1
12
Note. — The Sellers hob is designed to be run on centers, the
work, such as hand or die chasers, being held against it and fed
along by the lathe carriage.
SQUARE THREAD TAPS
-D —
-E
77
>f-FH
Standard Square-Thread Taps
Size
A
B
c
D
E
F
G
H
I
Diameter f. .d)
(2)
Pitch 8 (3)
Diameter f^.-d)
(2)
Pitch 6 (3)
Diameter f". .(i)
(2)
Pitch 4I (3)
Diameter i". .(i)
(2)
LeadD'BLr(3)
Diameter ij. . (i)
(2)
(3)
Pitch 3i (4)
Diameter if" .(i)
(2)
(3)
LeadD'BL i" (4)
If
¥
It
I
It
rr
f
47
it
If
¥
itV
li
lit
itV
h
ii
II
li
li
If
if
li
i4
li
li
4
3l
3f
3!
3l
4
4
4
4l
4i
4i
4f
4l
4f
4i
5i
5i
5i
5i
3i
3i
3i
3f
3f
3f
3f
3f
4i
fi
4f
4f
4l
4l
4f
4f
4f
4f
f
t\
ft
3
4
f
f
if
II
it
li
l|
li
li
1
f
f
f
f
1
1
li
li
li
li
If
If
If
If
ii
h
h
1
f
f
if
il
i
1
7
8
1
Note. — While in theory the thread and the space are both one
half the pitch in practice it is necessary to make the thread a little
more than half in order to allow clearance for the screw that goes
into the threaded hole. The amount of this clearance depends on
the character of the work and varies from .001 inch up. Some also
make the tap so that the screw will only bear on the top or bottom
and the sides.
FILES
Files are designated both by the spacing of their teeth and the-
shape or cross-section of steel on which the teeth are cut; the size
always referring to their length which is measured from the point
cutting to the end of the file proper but the measurement never
includes the tang which fits into the handle.
Terms Used
The back of a file is the convex or rounding side of half-round,
cabinet and other files having a similar shape.
A file is Bellied when it is full or large in the center.
A Blunt file is the same size its whole length instead of being tapered.
An Equalling file is one which looks blunt but which has a slight
belly or curve from joint to tang.
A Float file is a coarse single cut made for use on soft metals or
wood and frequently used by plumbers.
A Safe-edge is an edge left smooth or blank so that the file will not
cut if it strikes against the side of a slot or similar work.
The Tang is the small pointed end forged down for fitting into the
handle.
Three square files are double cut and have teeth only on the sides,
while taper saw files are usually single cut and have teeth on the
edge as well as the sides. This makes the taper saw files broad on
the edge or without sharp corners, while the three square files have
very sharp corners.
A special angle tooth file is made for brass work. The first cut is
square across the file, while the second is at quite an acute angle,
about 60 degrees from the first cut.
Doctor files are very similar to these except that the first cut is
about 15 degrees instead of being square across the file.
A lock file has safe edge and the teeth only go about one third the
way across from each side leaving the center blank. The teeth are
single cut.
HiGHT OF Work
The work should be at a convenient hight which will usually vary
from 40 to 44 inches for most men with an average of 42 inches.
This means the hight of the work, not the bench.
Pickling Bath
A good pickle to soften and loosen the scale on cast iron before
filing is made of two or three parts of water to one part of sulphuric
acid. Immerse castings for a short time.
For brass castings use a pickle of five parts water to one part nitric
acid.
78
TOOTH SPACING
79
BASTARD
r
SECOND CUT SMOOTH
Actual Tooth Spacing of Single Cut Files
SMOOTH DEAD SMOOTH
Actual Tooth Spacing of Double Cut Files
8o FILES
The Teeth of Files
The cut of a file or the number of teeth per inch vary with the
length of the file itself and the kind of a file, and is a little confusing,
as a rough cut in a small file may be as fine as a second cut of a
larger size. The cuts used on regular 12-inch files are shown in the
illustration and represents the practice of Henry Disston & Sons.
The same makers also supply the table of cuts per inch used on their
machines, which are as follows: ^
Regular Taper Files
Length, inches. — 2^, 3, 3!, 4, 4*, 5, 5 J, 6, 6^, 7, 8, 9, 10,
Teeth per inch — 64, 56, 52, 50, 48, 46, 44, 42, 42, 40, 38, 36, 34.
Slim Tapers — 64, 64, 60, 58, 56, 52, 50, 50, 46, 46, 44, 40, ^S.
Mill File, Bastard Cut
Length — 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 20 in.
Teeth — 56, 50, 48, 46, 44, 42, 40, 38, 36, 34, 32, 30, 28, 26, 24, 22
per inch.
Flat File, Bastard Cut
48, 42, 38, 36, 32, 30, 26, 24, 22, 20, 20, 18, 18, 16, 16, 14.
Single cut files usually have teeih at about 25 degrees and in double-
cut files the other cut is usually from 45 to 50 degrees. Fine
machinists files are made in ten numbers from 00 to 8.
The Shapes of Files
In the following pages the shapes of standard files are shown.
The names are as follows:
1. Metal saw — blunt. 6. Round or rat-tail. 12. Warding.
2. Three-square or tri- 7. Pippin. 13. Extra narrow
angular. 8 Knife. pillar.
3. Barrette. 9. Crossing. 14. Narrow pillar.
4. Slitting, 10. Half-round. 15 Pillar.
5. Square. 11. Crochet. 16 Hand.
Files are cut in two ways, single and double The first has but a
single line of cuts across the surface, at an angle with the file body
but parallel to each other. The double-cut file has two lines of cuts,
at an angle with each other, and the second cut being usually finer
than the first. Some prefer the single cut, for filing in the lathe.
Rasps have single teeth forced up with a punch.
The old method of designating the cuts were rough, coarse, bas-
tard, second cut, smooth and dead smooth. . Some makers are now
using a series of numbers — usually eight to ten — instead of
the six designations by name formerly employed. The uses of the
various cuts depend on the shop in question and m.ust be learned from
observation and experience in each case.
The grades of cut used by them run from No 00 to No. 8, and while
it is hard to exactly compare them with the old-style designations, it
will be found that No. 00 is about the same as a bastard. No. i as a
second cut, No. 2 or 3 with a smooth, and Nos. 6 to 8 with a dead
smooth file.
SHAPES OF FILES
8l
<]
<]
0
n
y v,,ij:wwMs.
The Standard Shapes of Files
82
FILES
Wf'
¥/W^'f.''yf/f'''yf>)!f/'^j,/y//^l:'W''J'-y 'ff/f,yy,,,/J>^^^^^^ . , .„,.m)^y.
\ ■ i
13
14
15
0
The Standard Shapes of Files
When a File Cuts Best
One who has given the matter careful attention, and has built
file-testing machines, Edward G. Herbert, of Manchester, England,
has come to the conclusion that a file does not cut best when it is
new but after it has been used for some little time, say 2500 strokes
or the filing away of one cubic inch of metal. Another curious
feature is that its usefulness seems to come to a sudden instead of a
gradual end.
A bastard file having 25 teeth to the inch, operating on a surface
one inch square with a pressure of 30 pounds, which is about equal
to heavy hand filing, gives 25 cutting edges about one inch long,
which likens it somewhat to a broad cutting tool in a planer.
In cutting a file the metal is forced up in a sort of a bur, and occa-
sionally the top of the tooth slopes over backward which is the reason
that a file often cuts better after these are broken or worn off. Then,
too, when a file is new all the teeth are not of the same hight and
only a few points cut. As they wear down more teeth come into
contact and do more work.
SMALL FILES
83
:wmMwmfmm/!m& ,r
r-
--— .„-:_„-^,.-.^..^.„_^Stt:.;^
1
■ii
)
La_
)
... J
K*
WSfM^^SS!:!i:!:::;L :
J
Needle Files for Fine Work
==^
^^^
Die Sinkers Files or Riffles
84
WORK BENCHES
WORK BENCHES
The duties of a bench vary with the shop in which it is located
according to the work that is to be done on it or at it. If it is simply
a fihng bench, the main requirement is that it support a vise firmly
and at the proper hight. If an assembling bench, these are not the
important features, and just what it does need depends on the kind
of work being handled.
For the average shop work we want a bench that is rigid; that will
stand chipping and filing; that can be used in testing work on a
surface plate or in handling jigs and fixtures; that will not splinter
badly nor yet injure a tool should it happen to drop on it. For the
toolmaker the cast-iron bench top has many advantages, but both
the bench and the tool are very liable to be marred by dropping the
tool on it, so that for general use we rely on wood as in the days of
old, except that a bench with solid 2- or 3-inch planking the whole
width is now too expensive to consider. We no longer want the
bench braced up against the side of the shop but set it out from
JFIG. 1. Good for Ordinary Work
FIG. 2. Another Method.
the wall to allow the heat to rise and the air to circulate, as well as
giving the sprinklers a chance to get at a fire on the floor near the
walls.
The use of a lighter board at the back has become so common that
the New Britain Machine Company's design for a bench leg is made
for this construction as shown in Fig. i. This also shows the back-
board B rabbeted to the plank A, which supports it all along the
front edge, and it is also supported by the stringer D, which runs the
whole length of the bench. These supports, in addition to the cross
bearing of the legs every 6 or 8 feet, give the backboard a stifl'ness
that was unknown where they are simply laid flush and not rabbeted
and the stringer is absent.
Benches made without these supports are open to the serious objec-
tion that the backboard springs down when a heavy weight, such as
a jig or surface plate, is put on the bench and throws them out of
level.
All cracks are more or less of a nuisance in bench work, but in
this case any shrinkage can be taken up by wedging against the
iron, support of the board C and the edge of the backboard B.
WORK BENCHES
8S
Another style bench with this same leg is shown in Fig. 2, Here
the front plank A and the backboard C are the same as before, but
instead of having one backboard, this part of the bench is made up
of narrow strips as B, fitting into rabbet in plank A and supported
by the stringer D as before. These narrow boards can be either
tongued and grooved hardwood flooring, or can be square edges, as
preferred; in either case any shrinkage can be taken up by forcing
the boards together.
A cheaper form of bench is shown in Fig. 3, where the heavy
planking is entirely dispensed with and the boards B run the full
width of the bench as shown. Running along the front, underneath
the main boards is a soft plank A which supports the edge of the
bench where the most work comes, and under the back is the 2X6-
inch stringer as before. Here, too, the boards can be either notched
or square edge, each having its advocates; the objection raised
against the tongue and groove being that the edges are apt to split
off from heavy articles dropping on them. An advantage claimed
for the boards running this way is that work going on or off the
FIG. 3. A Cheaper Way.
FIG. 4. A good but
expensive Construction.
bench is always in the direction of the grain of the wood and that
fewer splinters are formed on that account. In either Figs. 2 or 3
any local wear can be remedied by replacing the worn board with a
new one. Some object to the end of the grain at the front of a bench.
The material used in any of these can be varied to suit the indi-
vidual requirements. Maple is generally considered the best wood
for a bench, while others prefer ash. For the backboards hard pine
is often used and even cheaper woods will answer if necessary, al-
though it probably pays to use maple all through if you can afford
it.
Still another style of bench is shown in Fig. 4 and one which was
designed to be serviceable and have a long life without so much
regard to first cost as the others. The bench leg was flat on top,
the first layer of maple planks A and D and on top, narrower boards
of the same material. These were fastened with long wood screws,
holes being countered and plugged as shown.
The theory of this construction is that the boards are sure to be
more thoroughly seasoned than the planks, consequently the planks
86 SOLDERINCi
will shrink the most and tend to draw the top boards closer together.
It certainly makes a solid bench, but the first cost is rather high.
Benches are also occasionally built up from small blocks so as to
present an end grain on the top, the same as butchers' blocks. One
shop we know of surfaces these when worn by putting them on a
Daniels' planer and substituting a circular saw for the swinging
knives. This saws the top very smooth and leaves a good surface.
Others glue up strips on edge and plane down to a smooth surface
so as to do away with all cracks. Zinc or even heavy paper covers
are often used where fine work is being assembled to prevent its
finding its way into cracks and crevices.
The usual work bench is from ^^ to 35 inches from the floor to the
top, abolit 29 or 30 inches wide, and has the front plank 3 inches with
backboards i inch thick. A cast-iron leg of this type weighs about
50 pounds.
SOLDERING
Almost every one thinks he can solder, yet if we examine the
work carefully we will find that only about 10 per cent of the work
is really done as it should be. Thorough soldering is frequently
referred to as sweating, and it is remarkable the difference in strength
between a well-fitted and "sweated" junction of the metals and
one as ordinarily soldered.
A point frequently overlooked is the important one of properly
cleaning the surfaces to be joined. This is too often left for the
flux to correct. Another neglected point is the selection of the flux
to be used, although nearly all of the metals can be joined by the use
of the same flux. The after effects resulting from improper cleaning
after soldering are frequently worse than the good effects of the
soldering. This is particularly noticeable in electrical work.
For strength, fit the parts accurately. The more accurate the
fitting the stronger the result. Use a solder with as high a melting
point as possible. Apply the proper heat as it should be. The
nearer the temperature of work to be joined is brought to the fusing
point of the solder the better will be the union, since the solder will
flow more readily.
Fluxes for Different Metals
There are on the market a number of fluxes or soldering salts
that are giving good satisfaction. A form that is non-corrosive
and very popular with electrical workers is the soldering stick in
which the ingredients are molded into stick form about i inch diam-
eter and 6 inches long.
The action and use of a flux in soldering are to remove and pre-
vent the formation of an oxide during the operation of soldering,
and to allow the solder to flow readily and to unite more firmly
with the surfaces to be joined.
For sheet tin, on the best work rosin or colophony is used; but
owing to the ease of applying and rapidity of working, zinc chloride
SOLDERING 87
or acid is more generally used. Beeswax can also be used, as also
almost any of the pastes, fats or liquids prepared for the purpose.
For lead, a flux of oil and rosin in equal parts works very well.
Tallow is also a good flux. Rosin or colophony is much used, and
zinc chloride will keep the surfaces in good condition.
Lead burning is a different operation from soldering, and at the
present time almost a lost art. The surfaces must be bright and
free from oxide; solder is not used as a flux, but a piece of lead and
rosin or oil.
For brass, zinc chloride or almost any of the soldering prepara-
tions is used. Care must be taken to remove any scale or oxide
if a good joint is wanted. On new metal this is not much trouble,
but on old or repair work it is sometimes exceedingly difficult. This
is particularly noticeable on metal patterns that have been in use
for some time. The scraper must be brought into use to remove it.
Many use with considerable success an acid dip such as is com-
monly used by electro platers, for removing the oxide. Oily or
greasy work can be cleaned by the use of potash or lye, but care
must be exercised that the brass is not left too long in the solution,
especially if it contains any joints previously soldered, since the
action set up will dissolve the solder entirely or roughen up the
joint to such an extent as to require refinishing.
For copper, the same fluxes as for brass are used. On old work
it is almost always necessary to scrape the parts to be joined to get
the solder to hold. A particularly difficult piece of work to solder
is an old bath tub. The grease and soap form a layer that is imper-
vious to any of the fluxes, and it must be carefully removed entirely
if good work is wanted.
For zinc, use muriatic acid almost full strength or chloride of
zinc solution. Zinc is the metal that has a "critical temperature"
more than any other metal except the softer alloys. If the iron is
overheated, the zinc is melted and a hole burned in the metal;
even if this does not occur, the surface of the metal is roughened
and there is formed on the soldering copper an alloy that will not
flow but simply makes a pasty mass. At the correct heat the solder
will flow readily and unite firmly with the metal. Especially if
the work is to be painted, care should be taken to neutraUze and
wash off any excess of acid or soldering solution, as it is impossible
to cause paint to adhere properly unless this is done.
For galvanized iron, use muriatic acid, chloride of zinc solution
or rosin, and be sure to see that the acid is neutralized if the work
is to be painted. Many cornices and fronts are made of this metal
and are very unsightly in a short time after being painted, particu-
larly at the joints, owing to lack of care in removing the excess flux.
An action that is not usually taken into consideration in the joining
of galvanized iron or zinc with copper, as is sometimes done, is the
electrical action set up by the metals if any moisture is present.
This is very noticeable in cities where the acid from the atmosphere
assists in the action. It will nearly always be found that the zine
or galvanized iron has been greatly injured at the places joined.
For wrought iron or steel, zinc chloride is best. The iron or steel,
to make good work, should be previously freed from scale or oxide
88 SOLDERING
and tinned before joining. Where the oxide is not very heavy,
the iron can be cleaned by brushing with muriatic acid and rubbing
with a piece of zinc.
The Fluxes Themselves
The above paragraphs give the fluxes adapted to the various
metals; the fluxes themselves are as follows:
Hydrochloric or muriatic acid. The ordinary commercial acid
is much used in full strength or slightly diluted to solder zinc, par-
ticularly where the zinc is old or covered with an oxide.
Rosin or colophony, powdered, is commonly used for copper, tin
and lead, and very generally by canneries and packing houses on
account of its non -poisonous qualities. It is also used mixed with
common olive oil. Turpentine can also be used as a flux. Beeswax
is a good but expensive flux. Tallow is also used for lead pipe,
but is more frequently mixed with rosin.
Palm or cocoa oil will work well, but is more generally used in
the manufacture of tin plate. The common green oUve oil works
very well with the more fusible solders.
As expedients we can use a piece of common stearine candle or
a piece of common brown rosin soap or cheap furniture varnish,
which is largely composed of rosin. Paraffin, vaseline and stearine
are recommended for use with some of the alloys for soldering alu-
minum.
Chloride of zinc, acid, or soldering liquid, is the most commonly
used of all the fluxes; as usually prepared, simply dissolve as much
scrap zinc in the ordinary commercial muriatic acid as it will take
up. But if it is diluted with an equal quantity of water and a small
quantity of sal ammoniac is added it works much better and is less
likely to rust the articles soldered. If they are of iron or steel, about
2 ounces to the pint of solution is about the proper quantity of pow-
dered sal ammoniac to add.
In preparing this solution, a glass or porcelain vessel should be
used; owing to the corrosive fumes, it should be done in a well- ven-
tilated place. Use a vessel of ample capacity, since there is con-
siderable foaming or boiling of the mixture.
Soldering liquid, non-corrosive, is also prepared by dissolving
the zinc in the acid as above and adding one fourth of the quantity
of aqua ammonia to neutralize the acid, then diluting with an equal
quantity of water.
Soldering liquid, neither corrosive nor poisonous. Dissolve ij
parts glycerin, 12 parts water, and add i\ parts lactic acid.
Soldering paste. When a solution of chloride is mixed with starch
paste, a syrupy Hquid is formed which makes a flux for soldering.
Soldering fat or paste. Melt i pound of tallow and add I pound
of common olive oil. Stir in 8 ounces of powdered rosin; let this
boil up and when partially cool, add with constant stirring, \ pint
of water that has been saturated with powdered sal ammoniac.
Stir constantly until cool. By adding more rosin to make it harder,
this can be formed into sticks. A very good acid mixture for clean-
ing work to be soldered is equal parts of nitric and sulphuric acid
and water. Never pour the water into the acid.
SOLDERING CAST IRON
Cleaning and Holding Work
89
For copper work a dilute sulphuric acid is best. Articles of lead
and zinc can be cleaned with a potash solution, but care must be
exercised as the alkalies attack these metals. For zinc, a dilute
solution of sulphuric or muriatic acid will clean the surface.
For cleaning or removing the oxide or other foreign material,
scrapers and files are frequently used. An old file bent at the ends
and with the comers flaring makes a handy tool. Grind the edge
sharp and make as hard as possible.
To enable difficult points to be "filled," sometimes a small piece
of moist clay pressed into shape to form the desired shape can be
used to advantage as a guide for the solder. Another use of the
clay is to embed the parts in, to hold them in position for soldering.
Plaster of paris is also used for this purpose, but is sometimes
difiicult to remove, especially in hollow pieces. A dilute solution
of muriatic acid will help to get this out, however.
Castings containing aluminum are always harder to solder than
other alloys. In some instances where the percentage of aluminum
is high, it is necessary to copperplate the parts to be joined before
a satisfactory joint can be made. In nearly every instance the work
can be "stuck" together, but not actually soldered.
In metal-pattern making too little attention is given to both the
fitting of the parts and the selection of the solder to joint the work.
A good grade should always be used, and it must be borne in mind
that the higher the melting point of the solder the stronger the joint.
A very good job of soldering can be done on work that will permit
of it by carefully fitting the parts, laying a piece of tin foil, covered
on both sides with a flux, between the parts to be joined and pressing
them tightly together. Heat until the foil is melted. This is very
good in joining broken parts of brass and bronze work. If they
fit well together, they can frequently be joined in this manner so
that the joint is very strong and almost imperceptible.
Soldering Cast Iron
For cast iron, the flux is usually regarded as a secret. A number
of methods are in use; one of the oldest and least satisfactory is to
brush the surfaces thoroughly with a brass scratch brush. Brush
until the surface is coated with brass, then tin this surface and solder
as usual. If plating facilities are to be had, copperplate the parts
and solder together. This method has been used very successfully
for a number of years.
A fair substitute for the above is to clean the surfaces thoroughly
and copperplate them with a solution of sulphate of copper: about
I ounce sulphate of copper, \ pint water, ^ ounce sulphuric acid.
Brush this solution on or dip into the solution, rinse off and dry it
well before soldering.
Another method is to tin the cast iron. To do this, first remove
all scale until the surface is clean and bright. The easiest way to
do this is with the emery wheel. Dip in a lye to remove any grease,
and rinse the lye off; then dip into muriatic acid of the usual strength.
90 SOLDERING
Then go over the surface with rosin and a half and half solder. It
may be necessary to dip into the acid several times to get the piece
thoroughly tinned. Rubbing the surface of the iron with a piece
of zinc while the acid is still on it will facilitate the tinning.
Another method of soldering cast iron is to clean the surface as
in the previous operation and then brush over with chloride of zinc
solution and sprinkle powdered sal ammoniac on it; then heat until
the sal ammoniac smokes. Dip into melted tin and remove the
surplus; repeat if not thoroughly tinned. Half tin and half lead
works well as a solder for this.
Commutator wires and electrical connections should never be sol-
dered by using an acid solution, owing to the corrosive action after-
ward. A good flux is an alcoholic solution of rosin.
Cold Soldering for Metals, Glass, Porcelain, etc.
Precipitate the copper froiji a solution of the sulphate by putting
in strips of zinc. Place the copper powder in a porcelain or wedge-
wood mortar and mix it with from 20 to 30 parts of sulphuric acid
of 1.85 degrees Baume. Then add 70 parts of mercury when well
mixed, wash well with water to remove the excess of acid and allow
it to cool. To use it, heat it and pound it well in an iron mortar
until it becomes plastic. It can then be used and adheres very firmly
when cold. No flux is needed, but the surfaces must be clean. This
is used where heat cannot be used, or to join metal parts to glass or
porcelain.
A solution of copper for copperplating steel or cast iron before
soldering will work by simply immersing the work in it. This is
also useful to copper the surface of dies and tools to enable the me-
chanic to "lay out" or scribe the work so that the lines can be readily
seen. Take copper sulphate 3I ounces, sulphuric acid 3^ ounces,
water i to 2 gallons. Dissolve the copper in the water and add the
acid.
Solders and Fusible Alloys
Solders act under constant stress considerably like plastic or semi-
fluid material. Their fluidity resembles that of tar or gum, and their
distortion with time is greater than would be thought. In a series
of tests a notable point brought out was the varying degrees of
strength with age. Tensile strength increases with the percentage of
tin present, but when the solder's age is considered as a factor, the
product possesses its maximum value at 60 per cent, tin, showing this
property as similar to that of the melting point and depending upon
chemical composition.
For general work, the solder requiring resistance to stress is 60
per cent, tin, but for work requiring little mechanical strength, such
as sealing, a lower per cent, of tin may be used.
Generally speaking, all solders are alloys of lead and tin. The more
lead the alloy contains, above 40 per cent., the higher is its melting
point, as also the less lead it contains, below 40 per cent., the lower
is its melting point.
SOLDERING
91
The melting point of alloys which fuse at a low temperature may
be found by tying a small wire around a fragment of alloy and hang-
ing it in a bath of water. A thermometer should be kept in the bath
and the temperature increased slowly until the alloy melts. The melt-
ing point of the alloy can then be noted by the temperature of the
bath. For higher temperature a bath of paraffin or oil is used. If
bismuth is added to these alloys the melting point is lower, as bismuth
possesses the quality of expanding on cooling, a property which is
very unusual in metals. Bismuth is used not only to make the alloy
or solder more easily worked, by diminishing its melting point, but
if sufficient quantity be present its expansive tendency counter-
balances the effects of the contraction of the other metals, and the
total result is the prevention or reduction of shrinkage in the mold.
The addition of cadmium still farther lowers the melting point of such
alloys as those of bismuth, lead and tin, which in themselves have
very low melting points.
Composition and Melting Point of Solders and Fusible
Alloys
Alloy
Lead
Tin
Bis-
muth
Other
Constitu-
ents
Melting Point
Cent.
Fahr.
Solder i
96.15
90.9
83.3
75-0
66.7
50.0
40.0
33-3
33-3
48.4
44.5
42.1
10. 0
30.0
31-25
28.1
25.0
25.0
26.9
66.7
3-85
9.1
16.7
25-9
33-3
50.0
60.0
66.7
33-3
40.0
20.0
18.75
21.9
25.0
12.5
12.7
33-3
12.8
22.2
42.1
50.0
50.0
50.0
50.0
50.0
50.0
50.0
8.3
Zinc
38.8
33-3
15-8
Cadmium
12. 5
10.4
25.0
292
283
266
250
227
188
168
171
140
171
141
123
116
100
98
95
93
60
66
66
558
Solder 2
')4I
Solder 3
511
482
Solder 4
Solder 5
Solder 6
441
370
Solder 7
334
Solder 8
340
Solder g
284
1. Steam boiler plug
2. Steam boiler plug .
3. Steam boiler plug .
4. Steam boiler plug .
Sir Isaac Newton's.
Suitable for casts .
Rose's alloy
D'Arcet's alloy . . .
Wood's alloy
Lipowitz's alloy . .
Expanding alloy . .
340
285
253
240
212
208
203
200
140
150
150
Hard solders sometimes contain more or less copper. A substan-
tial solder contains 60 per cent, copper, 20 per cent, tin and 20 per
cent. zinc. An easily melted yellow, hard solder contains about 45
per cent, copper and 55 per cent. zinc. This solder is really a brass,
but at times is used for soldering, binding and filling purposes.
92 SOLDERING
Nearly all aluminum solders are alloys of tin and aluminum that
contain from 15 to 25 per cent, aluminum. A small per cent, of cop-
per or nickel, never exceeding 2 or 3 per cent., is sometimes used.
The exact point of separation between a fusible metal and a non-
fusible one is very uncertain, thus several additional alloys are given
in the table. In filling up imperfections in ornamental castings for
plugs in electrical wiring and on boilers in engineering work, fusible
alloys are used. Sometimes defects in structural steel have been
filled in with expanding alloy, after being dressed in a coat of point.
The United States Government rules call for pure Banca tin for boiler
plugs, but this is not essential and an}- good tin will serve the purpose.
Experiments have been made in an engineering college quite recently
for the purpose of finding the way of making solder joints, as well as
measuring their tensile strength. Any pressure upon the solder at
the moment of setting diminishes the strength of the joint. Thus, in
making a solder joint, the upper piece should be held above the lower
one, the solder fused by means of two blow torches, and the pieces
brought together by very slow and easy pressure. By employing this
method, which differs from that commonly called "sweating," the
joint is less liable to be broken, as the crystalline composition of
the resulting mass contains less resistance at this time.
In addition it is found that there is remarkable variation with time
of the tensile strength of such joints, which is also in accord with
what would be considered proper by engineering science in this field.
Under any circumstances the average strength attained does not
exceed 27,000 pounds per square inch, and was obtained from solder
made with three-fifths of its composition tin.
ARSENAL "HOT DLP" PROCESS FOR TINNING
Use a metal composed of 80 parts of lead to 20 parts of tin by
weight. The steel plate to be tinned is first pickled in a bath of
40 parts of water to one part of sulphuric acid by volume. After
pickling, the metal is washed in clean water to remove all traces
of the pickling acid. The work is then dipped in a flux which is
made b}'' dissolving zinc in hydrochloric acid until it is saturated.
After dipping in the flux, the pieces are dipped in the melted metal
(80% lead — 20% tin) until thoroughly coated and are then
shaken off and thrown in a pile to cool.
A Method of Tinning Brass Parts
Brass parts are placed in layers in a screened basket with tin
plates between each layer. They are then placed in a copper tank
filled with water supplied wnth steam coil and brought to a boiling
point. Sufficient amount of Cream of Tartar is added until the
parts are properly plated. Four hours are required to properly
tin these parts.
Small parts are placed in a cheese cloth bag in a solution of one
pint of phosphoric acid (U.S.P. 50% ) to four gallons of water. Heat
to a boiling point until pins begin to turn white, requiring about
two hours. Remove and place in linseed oil. They are then
rolled on staw boards to remove the surplus oil.
GEARING
GEAR TEETH — SHAPES OF
Cycloidal or Epicycloidal. — A curved tooth generated by the point
of a circle rolling away from the gear wheel or rack.
Involute. — A curved tooth generated by unwinding a tape or
string from a cylinder. The rack tooth has straight sides.
Involute Standard. — The standard gear tooth has a 14^ degree
pressure angle which means that the teeth of a standard rack have
straight sides 14J degrees from the vertical.
Involute — Stubbed. — A tooth shorter than the standard and
usually with a 20-degree pressure angle.
GEARS— TEETH AND PARTS
^ t<^ CireuJar
I I
1- * Measured on tho Ktch Circle
Fig. I. — Part of Gear Teeth
Addendum. — Length from pitch line to outside.
Chordal Pitch. — Distance from center to center of teeth in a
straight line.
Circular Pitch. — Distance from center to center of teeth meas-
ured on the pitch circle.
Clearance. — Extra depth of space between teeth.
Dedendum. — Length from pitch line to base of tooth.
Diametral Pitch. — Number of teeth divided by the pitch diam-
eter or the treth to each inch of diameter.
Face. — Working surface of tooth outside of pitch line.
Flank. • — Working surface of tooth below pitch line.
Outside Diameter. — Total diameter over teeth.
Pitch Diameter. — Diameter at the pitch line.
Pitch Line. — Line of contact of two cylinders which would have
the same speed ratios as the gears.
Linear Pitch. — Sometimes used in rack measurement. Same as
circular pitch of a gear.
S3
94
CIRCULAR PITCH
Having
The Diametral ,
Pitch I
The Pitch Di-1
ameter and I
the Number [
of Teeth ... J
The Outside 1
Diameter and I
the Number [
of Teeth ... J
The Number 1
of Teeth and I
the Circular |
Pitch J
The Number ]
of Teeth and (
the Outside |
Diameter ... J
The Outside ]
Diameter and I
the Circular |
Pitch J
Addendum and"]
the Number [
of Teeth ... J
The Number ]
of Teeth and I
the Circular [
Pitch J
The Pitch Di-I
ameter and I
the Circular [
Pitch J
The Number 1
of Teeth and I
the Adden- |
dum J
The Pitch Di-l
ameter and I
the Circular |
Pitch J
The Circular )
Pitch >
The Circular )
Pitch 5
The Circular )
Pitch )
The Circular )
Pitch i
The Circular 1
Pitch 5
The Circular )
Pitch 5
Thickness of \
Tooth '
To Get
The Circular
Pitch
The Circular
Pitch
The Circular
Pitch
Pitch Diameter
Pitch Diameter
Pitch Diameter
Pitch Diameter
Outside Diameter
Outside Diameter
Outside Diameter
Number of Teeth
Thickness of
Tooth
Addendum
Root
Working Depth
Whole Depth
Clearance
Clearance
Rule
Di\'ide 3.1416 by the Di
ametral Pitch . . .
Divide Pitch Diameter by
the product of .3183 and
Number of Teeth
Divide Outside Diameter by
the product of .3183 and
Number of Teeth plus 2
The continued product of
the Number of Teeth, the
Circular Pitch and .3183
DiNade the product of Num-
ber of Teeth and Outside
Diameter by Number of
Teeth plus 2
Subtract from the Outside
Diameter the product of
the Circular Pitch and
.6366
Multiply the Number of
Teeth by the Addendum
The continued product of
the Number of Teeth plus
2. the Circular Pitch and
•3183
Add to the Pitch Diameter
the product of the Cir
cular Pitch and .6366. . .
Multiply Addendum by
Number of Teeth plus 2
Divide the product of Pitch
Diameter and 3.1416 by
the Circular Pitch
One half the Circular Pitch
Multiply the Circular Pitch
D'
by .3183 or 5 = —
Multiply the Circular Pitch
by .3683
Multiply the Circular Pitch
by .6366
Multiply the Circular Pitch
by .6866
Mutliply "the Circular Pitch
by .05
One tenth the Thickness of
Tooth at Pitch Line . . .
Formula
F
.3183 N
.3183 iV+ 2
P'=iVP'.3i83
N+2
D'=D~
iP'.6366]
D'=Ns
D=(N+2)
P' .3183
D =D'+
(i".6366)
D==s(N+2)
N
-P'3-i4i6
,=^
s-P-. iiS}
s+f=
P' .3683
D"=P
.6366
D"=P
.6866
f = P'
•05
f-\
DIAMETRAL PITCH
95
Having
The Circular
Pitch
The Pitch Di-
ameter and
the Number
of Teeth . . .
The Outside
Diameter and
the Number
of Teeth
The Number of
Teeth and
the Diametral
Pitch
The Number of
Teeth and the
Outside Di-
ameter
The Outside
Diameter and
the Diame-
tral Pitch . . . ,
Addendum and
the Number
of Teeth ... ^
The Number of
Teeth and the
D iametral
Pitch
ThePitchDiam-"
eter and the
Diametral
Pitch ,
The Pitch Di-
ameter and
the Number
of Teeth . . .
The Number of ]
Teeth and
Addendum . .
The Pitch Di-
ameter and
the Diametral
Pitch
The Outside '
Diameter and
the Diametral
Pitch
The Diametral
Pitch
The Diametral
Pitch
The Diametral
Pitch
The Diametral
Pitch
The Diametral
Pitch
The Diametral
Pitch
Thickness of i
Tooth
To Get
The Diametral
Pitch
The Diametral
Pitch
The Diametral
Pitch
Pitch Diameter
Pitch Diameter
Pitch Diameter
Pitch Diameter
Outside Diameter
Outside Diameter
Outside Diameter
Outside Diameter
Number of
Teeth
Number of
Teeth
Thickness of
Tooth
Addendum
Root
Working Depth
Whole Depth
Clearance
Clearance
Rule
Divide 3.1416 by the Cir
cular Pitch ,
Divide Number of Teeth by
Pitch Diameter
Divide Number of Teeth
plus 2 by Outside Di
ameter
Divide Number of Teeth by
the Diametral Pitch . .
Divide the Product of Out
side Diameter and Num
ber of Teeth by Number
of Teeth plus 2
Subtract from the Outside
Diameter the quotient of
2 divided by the Diametral
Pitch
Multiply Addendum by the^
Number of Teeth
Formula
3-1416
N
P =
N+2
D'--
DN
Divide Number of Teeth
plus 2 by the Diametral
Pitch
Add to the Pitch Diameter
the quotient of 2 divided
by the Diametral Pitch
Divide the Number of Teeth
plus 2, by the quotient of
number of Teeth divided
by Pitch Diameter . . .
Multiply the Number of
Teeth plus 2 by Adden
dum
Multiply Pitch Diameter by
the Diametral Pitch . .
Multiply Outside Diameter
by the Diametral Pitch
and subtract 2
Divide 1.5708 by the Di
ametral Pitch
Divide i by the Diametral
Pitch or J = TV
N
Divide 1.157 by the Diam-
etral Pitch
Divide 2 by the Diametral
Pitch
Divide 2.157 by the Dia-
metral Pitch
Divide .157 by the Diametral
Pitch
Divide Thickness of Tooth
at pitch hne by 10
N+2
iy=sN
D=D'
D =
P
N+2
N
D'
D=(N+2)s
N==D' P
N==DP-2
, 1-5708
^ - P
I
B"=i
D"+f
f
2-157
P
f
iL17
P
t
96 GEARING
Table of Corresponding Diametral and Circular Pitches
Table No. i
Table No. 2
Diametral
Pitch
Circular Pitch
Circular
Pitch
Diametral Pitch
li
2-5133
2
I-57I
I^
2.0944
i|
1.676
if
1-7952
If
1-795
2
I-57I
If
1-933
2i
1.396
li
2.094
2i
1-257
ItV
2.185
2|
1. 142
'K
2.285
3
1.047
lA
2.394
3^
.898
li
2-513
4
.7S5
lA
2.646
5
.628
i|
2-793
6
.524
ItV
2.957
7
.449
I
3.142
8
.393
if
3-351
9
•349
1
3-590
lO
.314
if
3.867
II
.286
f
4.189
12
.262
16
4-570
14
.224
f
5.027
i6
.196
T^.
5-585
i8
•175
i
6.283
20
.157
tV
7. 181
22
.143
t
8.378
24
•131
t\
10-053
26
.121
i
12.566
28
.112
^
16.755
30
.105
i
25-133
32
.098
tV
50.266
36
.087
40
.079
48
.065
No. I table shows the diametral pitches with the corresponding
circular pitches.
No. 2 table shows the circular pitches with the corresponding
diametral pitches.
It is most natui'al to think of gears in circular or linear pitch and
we soon get to know the size of any pitch, as 12, as being a little
over i inch from center to center. But the diametral system has
many advantages in figuring gear blanks, center distances, etc.
The Center Distance of any pair of spur gears is found by adding
one-half the pitch diameter of both gears.
CONSTANTS FOR CHORD AL PITCH
97
Constant for any number of teeth
CONSTANTS FOR DETERMINING CHORDAL PITCH AND
RADIUS OF SPUR GEARS
P = Chordal Pitch of Teeth.
R = Radius of Pitch Circle.
N = Number of Teeth.
C = Constant. (See table below.)
_, , , . , Radius of pitch circle
Chordal pitch = — \ ;: r.
Constant tor number oi teeth
Radius of pitch circle = Constant X chordal pitch.
Radius of pitch circle
Chordal pitch of teeth*
Examples : i . What is radius of pitch circle of a gear having 45 teeth,
if inch pitch? Follow 40 in table to column 5 (making 45 teeth),
and find 7.168. Multiply by pitch, if inch, and get 12.54 inches
radius or 25.08 pitch diameter.
2. What is the chordal pitch of a gear 32 inches pitch diameter,
67 teeth? Follow 60 in table to column 7 and find 10.668. Divide
radius (| of 32 = 16 inches) by constant. 16 ^ 10.668 = 1.5 inch
pitch.
3. What number of teeth has a gear of 1.5 inch chordal pitch and
pitch diameter 32 inches? Divide by 2 to get radius. Divide this
by chordal pitch which will give constant. 16-7- 1.5 = 10.666. Look
in table for this constant which will be found to represent 67 teeth.
Table of Constants
N
0
I
2
3
4
5
6
7
8
9
0
0.000
0.000
0.500
0.577
0.707
0.851
1. 000
1. 152
1-307
1.462
10
1.618
1.774
1.932
2.089
2.247
2.405
2-563
2.721
2.879
3-038
20
3.196
3.355
3-513
3.672
3.831
3.989
4.148
4-307
4-465
4.624
30
4.783
4.942
5.101
5.260
5.419
5.578
5-737
5.896
6.055
6.214
40
6.373
6.532
6.691
6.850
7.009
7.168
7-327
7.486
7.645
7.804
50
7-963
8.122
8.281
8.440
8.599
8.758
8.918
9.077
9.236
9-395
60
9-554
9.713
9.872
10.031
10.190
10.349
10.508
10.668
10.827
10.986
70
II. 145
IX. 304
11.463
11.622
II. 781
11.940
12.099
12.258
12.418
12.577
80
12.736
12.895
13.054
13.213
13.372
13-531
13.690
13.849
14.008
14.168
90
14-327
14-486 14.645
14.804
14.963
IS-123
15.282
15-441
15.600
15-759
100
15-918
16.077
16.236
16.395
16.554
16.713
16.873
17-032
17.191
17.350
no
17-509
17-668
17.828
17.987
18.146
18.305
18.464
18.624
18.783
18.942
120
19.101
19.260
19.419
19-579
19-738
19.897
20.056
20.215
20.375
20.534
130
20.693
20.852
2 1. 01 1
21.170
21.330
21.489
21.648
21.807
21.966
22.126
140
22.285
22.444
22.603
22.762
22.921
23.081
23.240
23-399
23-558
23.717
150
23-877
24.036
24.195
24-354
24-513
24.672
24.832
24.991
25-150
25.309
160
25.468
25.627
25-787
25-946
26.105
26.264
26.423
26.583
26.742
26.901
170
27.060
27.219
27-378
27-538
27.697
27.856
28.015
28.174
28.334
28.493
180
28.652
28.811
28.970
29.129
29.289
29.448
29.607
29.766
29.925
30.085
190
30-242
30.403
30.562
30.721
30.880
31.040
31-199
31-358
31-517
31-676
200
31-830
31.9S9
32-148
32.307
32.446
32-625
32.785
32.944
33-103
33-262
210
33-427
33-586
33-746
33-905
34.064
34-223
34.382
34-542
34.701
34-860
220
35-019
35-178
35-337
35-497
35-656
35-815
35-974
36.133
36-293
36-452
230
36.611
36.770
36.929
37.088
37-248
37-407
37-566
37-725
37-884
38.044
240
38.203
38.362
38.521
38.680
38-839
38-999
39-158
39-317
39-476
39635
250
39.7C5
98
GEARING
Gear Wheels
table of tooth parts diametral pitch in
[RST COLUMN
'^'t
*Mla,
•^
^.2
"o
f
•§
"S
1
^
13
S
1%
Q
'oS
a
1^
I3j
Msi
"2
^■B
^
6
6
1
M 0
&2
¥
s
u
H
<
^
Q
^
p
P'
t
s
D"
H-/
D"+/
h
6.2832
3.1416
2.0000
4.0000
2.3142
4.3142
f
4.1888
2.0944
T-?>m
2.6666
1.5428
2.8761
I
3.I4I6
1.5708
1. 0000
2.0000
I-1571
2.1571
li
2-5133
1.2566
.8000
1.6000
-9257
1-7257
li
2.0944
1.0472
.6666
^■?>3?>3
•7714
1-4381
If
1-7952
.8976
•5714
1. 1429
.6612
1.2326
2
1.5708
•7854
.5000
1. 0000
.5785
1.0785
2i
1-3963
.6981
-4444
.8888
.5143
.9587
2h
1.2566
.6283
.4000
.8000
.4628
.8628
2\
1. 1424
•5712
.3636
-7273
.4208
•7844
3
1.0472
-5236
•3333
.6666
-3857
.7190
?>h
.8976
.4488
.2857
-5714
•3306
.6163
4
.7854
-3927
.2500
.5000
.2893
•5393
5
.6283
.3142
.2000
.4000
.2314
-4314
6
•5236
.2618
.1666
■33,?,i
.1928
-3595
7
.4488
.2244
.1429
.2857
•1653
.3081
8
-3927
.1963
.1250
.2500
.1446
.2696
9
-3491
-1745
.iiii
.2222
.1286
•2397
lO
-3142
-1571
.1000
.2000
•I157
•2157
II
.2856
.1428
.0909
.1818
.1052
.1961
12
.2618
.1309
•0833
.1666
.0964
.1798
13
.2417
.1208
.0769
•1538
.0890
.1659
14
.2244
.1122
.0714
.1429
.0826
• 1541
To obtain the size of any part of a diametral pitch not given in the
table, divide the corresponding part of i diametral pitch by the pitch
required.
As it is natural to think of gear pitches as the distance between
teeth the same as threads, it is well to fix in the mind the approxi-
mate center distances of the pitches most in use. Or it is easy to
remember that if the diametral pitch be divided by 3I we have the
teeth per inch on the pitch line. By this method we easily see that
in a 10 diametral pitch gear there are approximately 3 teeth per inch
while in a 22 diametral pitch there will be just 7 teeth to the inch.
PARTS OF TEETH
99
Table of Tooth Parts — Continued
DIAMETRAL PITCH IN FIRST COLUMN
■^-s
*Hla.
*o
8S
'o
1
<u a
a °
1
1
!3
^^
T3
^:S
^
ji
a
.2
-^
3
.^
a
1^
M 0
&2
0 0
Q
0
H
^
^
Q
^
P
P'
/
s
D"
s+f
D"+f
15
2094
.1047
.0666
•1333
.0771
.1438
t6
1963
.0982
.0625
.1250
.0723
.1348
17
1848
.0924
.0588
.1176
.0681
.1269
i8
1745
.0873
•0555
.1111
.0643
.1198
19
1653
.0827
.0526
•1053
.0609
.1135
20
1571
.0785
.0500
.1000
•0579
.1079
22
1428
.0714
•0455
.0909
.0526
.0980
24
1309
.0654
.0417
•0833
.0482
.0898
26
1208
.0604
•0385
.0769
•0445
.0829
28
1122
.0561
•0357
.0714
■0413
.0770
30
1047
.0524
•0333
.0666
.0386
.0719
32
0982
.0491
.0312
.0625
.0362
.0674
34
0924
.0462
.0294
.0588
.0340
.0634
36
0873
.0436
.0278
•0555
.0321
•0599
38
0827
.0413
.0263
.0526
.0304
.0568
40
0785
.0393
.0250
.0500
.0289
•0539
42
0748
•0374
.0238
.0476
.0275
.0514
44
0714
•0357
.0227
•0455
.0263
.0490
46
0683
.0341
.0217
•0435
.0252
.0469
48
0654
.0327
.0208
.0417
.0241
.0449
50
0628
.0314
.0200
.0400
.0231
.0431
56
0561
.0280
.0178
•0357
.0207
.0385
60
0524
.0262
.0166
•0333
.0193
.0360
To obtain the size of any part of a diametral pitch not given in the
table, divide the corresponding part of i diametral pitch by the pitch
required.
As it is natural to think of gear pitches as the distance between
teeth the same as threads, it is well to fix in the mind the approxi-
mate center distances of the pitches most in use. Or it is easy to
remember that if the diametral pitch be divided by 3y we have the
teeth per inch on the pitch line. By this method we easily see that
in a 10 diametral pitch gear there are approximately 3 teeth per inch
while in a 22 diametral pitch there will be just 7 teeth to the inch.
100
GEARING
Gear Wheels
table of tooth parts — circular pitch in first column
I^H
"o-u
-0
^
8S
"o
-T3
T3
3
43
i-i
.5
-18
■5'S
5h°
1^
Q
r
P
r
1
S"^
r
P'
p
/
s
D"
s+f
D"+/
P'X.31
p'x.335
2
^
1.5708
1. 0000
.6366
1.2732
.7366
1-3732
.6200
.6700
If
tV
1-6755
•9375
.5968
1^1937
.6906
1.2874
.5813
.6281
If
f
1-7952
.8750
•5570
1.1141
•6445
1. 2016
-5425
•5863
If
?
1-9333
.8125
-5173
1-0345
.5985
1.1158
.5038
•5444
I^
f
2.0944
.7500
-4775
.9549
•5525
1.0299
.4650
•5025
itV
if
2-1855
.7187
•4576
•9151
-5294
.9870
•4456
.4816
if
tV
2.2848
•6875
-4377
.8754
•5064
.9441
.4262
.4606
li
1
2.3562
.6666
.4244
.8488
.4910
•9154
•4133
.4466
It\
M
2-3936
.6562
.4178
.8356
•4834
.9012
.4069
•4397
li
t
2.5133
.6250
-3979
.7958
.4604
•8583
•3875
.4188
ixV
if
2.6456
.5937
•3780
•7560
.4374
.8156
.3681
-3978
li
f
2.7925
•5625
•3581
.7162
.4143
•7724
.3488
•3769
ItV
if
2.9568
.5312
.3382
.6764
•3913
.7295
•3294
•3559
I
I
3-1416
,5000
•3183
.6366
•3683
.6866
.3100
•3350
H
itV
3-3510
-4687
.2984
.5968
•3453
•6437
.2906
.3141
i
li
3-5904
•4375
•2785
.5570
.3223
.6007
.2713
•2931
if
ItV
3.8666
.4062
.2586
•5173
•2993
•5579
.2519
.2722
f
li
3-9270
.4000
•2546
.5092
.2946
•5492
.2480
.2680
1
I*
4.1888
-3750
•2387
.4775
.2762
•5150
•2325
•2513
?
^p
4-5696
•3437
.2189
•4377
•2532
.4720
.2131
•2303
f
l\
4.7124
■2,333
.2122
.4244
•2455
.4577
.2066
•2233
1
If
5-0265
-3125
.1989
.3979
.2301
.4291
.1938
.2094
1
tS
5-2360
.3000
.1910
.3820
.2210
.4120
.i860
.2010
f
If
5-4978
•2857
.1819
•3638
.2105
•3923
.1771
.1914
t\
ll
5-5851
.2812
.1790
.3581
.2071
.3862
.1744
.1884
To obtain the size of any part of a circular pitch not given in the
table, multiply the corresponding part of i" pitch by the pitch re-
quired.
As an example take a gear having 21 diametral pitch to find the
various tooth parts. Take i diametral pitch and divide 3.1416 by
21 to find the corresponding circular pitch, which is .14951. The
tooth thickness is 1.5708 -^ 21 = .748; the addendum is i.-r- 21 =
©4761; the working depth is 2.-f- 21. = .09522; the depth below
PARTS OF TEETH
lOI
Table of Tooth Parts
circular pitch in first column
^!5
"^•3
T3
M
S§
•0
"U
T)
3
^1
e
.3
a
h
ft
w
1,8
0,
■^1
1^
u
h"^
Q
H
s
^
Q
^'
^
P'
P
/
D"
^4-/
D"+f
p'x.31
P'X.335
h
2
6.2832
.2500
-1592
.3183
.1842
.3433
.1550
-167s
1
2i
7.0685
.2222
•I4I5
.2830
•1637
•3052
•1378
.1489
tV
2f
7.1808
.2187
-1393
-2785
.1611
.3003
.1356
.1466
f
2*
7-3304
.2143
-1364
.2728
-1578
.2942
.1328
.1436
f
2i
7.8540
,2000
•1273
-2546
-1473
.2746
.1240
.1340
f
2§
8.3776
-1875
.1194
-2387
.1381
•2575
.1163
.1256
t\
2|
8.6394
.1818
.1158
-2316
.1340
.2498
.1127
.1218
i
3
9.4248
.1666
.1061
.2122
.1228
.2289
.1033
.1117
¥
3i
10.0531
.1562
-0995
.1989
.1151
,2146
.0969
.1047
1^
3i
10.4719
.1500
-0955
.1910
.1105
.2060
-0930
.1005
f
3^
10.9956
.1429
.0909
.1819
.1052
.1962
.0886
-0957
i
4
12.5664
.1250
.0796
•1591
.0921
.1716
-0775
.0838
f
4^
14.1372
.1111
.0707
•1415
.0818
.1526
.0689
-0744
t
5,
15.7080
.1000
-0637
-1273
•0737
•1373
.0620
.0670
♦
5i
16.7552
•0937
-0597
.1194
.0690
.1287
•0581
.0628
A
5i
17.2788
.0909
-0579
.1158
.0670
.1249
.0564
.0609
\
6
18.8496
•0833
-0531
.1061
.0614
.1144
•0517
-0558
^?
6i
20.4203
.0769
.0489
.0978
.0566
-1055
-0477
-0515
\
7
21.9911
.0714
-0455
.0910
.0526
.0981
-0443
-0479
^-E
lh
23.5619
.0666
•0425
.0850
.0492
.0917
.0414
.0446
\
8
25-1327
.0625
•0398
.0796
.0460
.0858
.0388
.0419
f
9
28.2743
•0555
•0354
.0707
.0409
.0763
-0344
.0372
tV
lO
31-4159
.0500
.0318
.0637
.0368
.0687
.0310
•0335
S^
i6
50-2655
.0312
.0199
.0398
.0230
.0429
.0194
.0209
^v
20
62.8318
.0250
•0159
.0318
.0184
.0343
•0155
.0167
To obtain the size of any part of a circular pitch not given in the
table, multiply the corresponding part of i'' pitch by the pitch re-
quired.
pitch line is 1.1571 -^ 21 = .0551 and the whole depth is 2.1571 -^
21 = .1027 inches. These could also have been obtained by split-
ting the difference between the figures for 20 and 22 pitch. The
same can be done for circular pitch except that we multiply instead
of divide.
I02
GEARING
DIAGRAM FOR CAST-GEAR TEETH
The accompanying diagram (Fig. 2) for laying out teeth for cast
gears will be found useful by the machinist, patternmaker and drafts-
man. The diagram for circular pitch gears is similar to the one
given by Professor Willis, while the one for diametral pitch was
obtained by using the relation of diametral to circular pitch.
Circular
LLlL
V 2"
J. I, I, I, III, 1, 1,1, 1, 1, J, I,
,1,1.1,1,1,1,1,1,1
Figs. 2 and
By the diagram the relative size of a tooth may be easily deter-
mined. For example, if we contemplate using a gear of 2 diametral
pitch, by referring to line H K, which shows the comparative distance
between centers of teeth, on the pitch line, it will be observed that
LAYING OUT SPUR GEAR BLANKS 103
2 diametral pitch is but little greater than i^ inches circular pitch,
or exactly 1.57 inches circular pitch. This result is obtained by
dividing 3.1416 by the diametral pitch (3.1416 divided by 2 equals
1.57). In similar manner, if the circular pitch is known, the diame-
tral pitch which corresponds to it is found by dividing 3. 141 6 by the
circular pitch; for example, the diametral pitch which corresponds
to 3 inches circular pitch is by the line H K a. little greater than i
diametral pitch, or exactly 1.047 (3.i4i6"divided by 3 equals 1.047).
. The proportions of a tooth may be determined for either diametral
or circular pitch by using the corresponding diagram.
Continue, for illustration, the 2 diametral pitch. We have found,
above, the distance betvv^een centers of teeth on the pitch line to be
a little more than ih inches (1.57 inches). The hight of tooth above
pitch line B' C will be found on the horizontal line corresponding
to 2 pitch. The distance between the lines A' B' and A' C on this
line may be taken in the dividers and transferred to the scale below.
Thus we find the hight of the tooth to be \% inch. In the same
manner the thickness of tooth B' D', width of space B' E', working
depth B' F' and whole depth of tooth B' G' may be determined.
The backlash or space between the idle surfaces of the teeth of
two gear wheels when in mesh is given by the distance D' E'. The
clearance or distance between the point of one tooth and the bottom
of space into which it meshes is given by the distance F' G' . The
backlash and clearance will vary according to the class of work for
which the gears are to be used and the accuracy of the molded pro-
duct. For machine molded gears which are to run in enclosed cases,
or where they may be kept well oiled and free from dirt, the backlash
and clearance may be reduced to a very small amount, while for
gears running where dirt is likely to get into the teeth, or where
irregularities due to molding, uneven shrinkage, and like causes, enter
into the construction, there must be a greater allowance. The
diagram is laid out for the latter case. Those who have more favor-
able conditions for which to design gears should vary the diagram
to suit their conditions. This can be done by increasing B D and
decreasing B E, and by increasing B C or decreasing B G, or both,
to get the clearance that will best meet the required conditions. The
same kind of diagram could be laid out for cut gears, but as tables
are usually at hand which give the dimensions of the parts of such
gears, figured to thousandths of an inch, it would be as well to consult
one of these.
LAYING OUT SPUR GEAR BLANKS
Decide upon the size wanted, remembering that 12-pitch teeth
are j\ deep and 8-pitch — as in the drawing — | deep, etc. Should
it be 8 pitch, as shown in the cut, draw a circle measuring as many
eighths of an inch in diameter as there are to be teeth in the gear.
This circle is called the Pitch Line. Then with a -radius J of an inch
larger, draw another circle from the same center, which will give
the outside diameter of the gear, or f larger than the pitch circle.
Thus we have for the diameter of an 8-pitch gear of 24 teeth, -2/-.
Should there be 16 teeth, as in the small spur gear in the cut, th?
I04
GEARING
outside diameter would be V? the number of teeth being always
two less than there are eighths — ivhen it is 8 pitch — in the outside
diameter.
The distance from the pitch line to the bottom of the teeth is the
same as to the top; excepting the clearance, which varies from \ of
the pitch to y^ of the thickness of the tooth at the pitch line. This
latter is used by Brown & Sharpe and many others, but the clearance,
being provided for in the cutters the two gears would be laid out to
mesh together just f .
These rules apply to all pitches, so that the outside diameter of
a 5-pitch gear with 24 teeth would be 3-; if a 3-pitch gear with 40
teeth it would be V'. Again, if a blank be 4I (%^) in diameter, and
cut 6 pitch, it should contain 23 teeth.
y^'UiQ^^ 8 Pitch - 24 Teeth
35i" Outside Diam.
Fig. 4. — Laying out a Pair of Gears
Actual Size of Diametral Pitches
It is not always easy to judge or imagine just how large a given
pitch is when measured by the diametral system. To make it easy
to see just what any pitch looks like the actual sizes of twelve di-
ametral pitches are given on the following page, ranging from 20
to 4 teeth per inch of diameter on the pitch line, so that a good idea
of the size of any of these teeth can be had at a glance.
ACTUAL SIZES OF GEAR TEETH 105
/\fvr\ (Myp^ |/w^
20 p.
18 P.
16 P.
^rvAA^ /vv^ f^^^
14 P..
12 P.
9 P.
7 F.
6 P.
5 P,
4^.
io6
GEARING
LAYING OUT SINGLE CURVE TOOTH
A VERY simple method of laying out a standard tooth is shown
in Fig. 5, and is known as the single curve method. Having calcu-
lated the various proportions of the tooth by rules already given,
draw the pitch, outside, working depth and clearance or whole depth
circles as shown. With a radius one half the pitch radius draw the
semicircle from the center to the pitch circle. Take one quarter
the pitch radius and with one leg at top of pitch circle strike arc
cutting the semicircle. This is the center for the first tooth curve
and locates the base circle for all the tooth arcs. Lay off the tooth
thickness and space distances around the pitch circle and draw the
tooth curves through these points with the tooth curve radius already
found. The fillets in the tooth corners may be taken as one seventh
of the space between the tops of the teeth.
Tooth Curve 'Rad^u^
One quarter of Pitch RadiUB
Fig. 5. — Single Curve Tooth
PRESSURE ANGLES
We next come to pressure angles of gear teeth, which means the
angle at which one tooth presses against the other and can best be
shown by the pinion and rack. Figs. 6 and 7.
The standard tooth has a 141 degree pressure angle, probably
because it was so easy for the millwright to lay it out as he could
obtain the angle without a protractor by using the method shown
for laying out a thread tool (see Fig. 14). As the sides of an involute
rack tooth are straight, and at the pressure angle from the perpen-
dicular, draw the line of pressure at 14^ degrees from the pitch line.
The base circle of the tooth arcs can be found by drawing a line
from the center of the gear to the line of pressure and at right angles
to it as shown, or by the first method, and working from this the tooth
STUB-TOOTH GEARS
107
curve can be drawn by either the single-curve method or, as is more
usual, by stopping the curv« from two or more points on this same
circle.
The difference between the 14^- and 20-degree pressure angles
can be seen by comparing Figs. 6 and 7. Not only is the tooth
shorter, but the base is broader. The base circle for the tooth arcs
is found in the same way as before.
This form of tooth is largely used in automobile transmission and
similar work. William Sellers & Co. use a 20 degree pressure
angle with a tooth of standard length.
Vy* Clesfrance or Bottom I \ Base Circle for Toolh Arcs
« V^ Working Pepth \ Pitch Circle —
Y iA ^4^- — Outside Diameter | \ ,
Fig. 6. — Standard Tooth
STUB-TOOTH GEARS
Any tooth shorter than the regular standard length is called a
"stub" tooth, but like the bastard thread there have been many
kinds. In 1899 the Fellows Gear Shaper Company introduced a
short tooth with a 20-degree pressure angle instead of the usual 14^-
degree. This gives a broader flank to the tooth and makes a stronger
gear, especially for small pinions where strength is needed. While
the Fellows tooth is shorter than the standard tooth there is no fixed
relation between them, as, on account of the tooth depth graduations
of the gear shaper, it was thought best to give the new tooth depth
in the same scale which is shown in the following table. This means
that if the pitch is 4 it has the depth of a 5-pitch standard tooth
divided as shown. The clearance is one-quarter the addendum or
dedendum.
io8
GEARING
Table of Tooth Dimensions of the Fellows Stub-Tooth Gear
fl
Stub
Tooth
Has Depth
of Standard
Thickness
on
Addendum
Dedendum and
Clearance
dt
Pitch
Tooth
Pitch Line
s
^
4
5
.3925
.200
.250
^
s
7
.314
.1429
•1785 •
1
6
8
.2617
.125
.1562
1
7
9
.2243
• III
.1389
^
8
lO
.1962
.100
.125
rV
9
II
.1744
.0909
.1137
H
lO
12
•157
.0S33
.1042
li
12
14
.1308
.0714
.0893
Fig. 7, — Stubbed Tooth
The Nuttall Company also use a 20-degree stub tooth, but have ai
fixed length or depth in the following proportions.
Addendum = .25 X circular pitch instead of .3683.
Dedendum = .30 X circular pitch instead of .3683.
Working depth = .50 X circular pitch instead of .6366.
Clearance >= .05 X circular pitch same as standard.
Whole depth = .55 X circular pitch instead of .6866.
SIZES OF GEAR BLANKS
109
Table for Turning and Cutting Gear Blanks
FOR standard length TOOTH
Pitch
16
1 12
10
8
Pitch
16
1 12
1 10
1 8
Depth
of Tooth
•135
.180
.216
.270
Depth
of Tooth
.135
.180
.216
.270
No. of
Teeth
Outside Diameter
No. of
Teeth
Outside Diameter
10
3
4
I
lA
I*
51
3A
4A
5x%
6f
II
if
irV
lA
If
52
3l
4A
5x%
6f
12
I
lA
lA
If
53
3A
•4A
5A
6|
13
if
lA
lA
li
54
Sh
4A
5x%
14
I
lA
lA
2
55
3A
4A
5A
7i
15
ItV
lA
lA
2i
56
^f.
4x1
5A
7i
16
li
it%
lA
2i
57
3H
4x-2-
5x%
7I
17
ItV
iiV
lA
2f
58
3f
5
6
7I
18
li
lA
2
2|
59
3if
5A
6A
7f
19
lA
lA
2A
2|
60
sl
5A
6A
7f
20
If
iM
2A
2f
61
3\%
5A
6A
7I
21
ItV
lii
2A
2i
62
4
5x%
6x^0
8
22
li
2
2A
3
63
4A
5A
6A
8i
23
I^
2A-
2A
3l
64
4j
5x^2
6A
8i
24
If
2A
2A
3i
65
4A
5A
6A
81
25
•lii
2A
2A
3f
66
4i
5x%
6A
8^
26
If
2A
2A
3i
67
f
6A
8f
27
lit
2A
2A
3l
68
5it
7
8f
28
Ij
2 A
3
3f
69
4A
5ii
7A
H
29
iM
2tV
3A
3i
70
4h
6
7A
9
30
2
2A
3A
4
71
4A
6A
ZaV
9i
31
2tV
2t%
3A
4i
72
4t
6x\
7x%
9i
32
2i
2M
3A
4i
73
4H
6A
7A
9l
33
2A
2^
3A
4f
74
4f
7*
9\
34
2i
3
3A
4i
75
4i|
6A
7xV
9l
35
2tV
3A
3A
4f
76
4i
6x'i
6x^3
7A
9f
36
2f
3A
3A
4f
77
4H
7A
9I
2>1
2tV
i
3A
4|
78
5
6A
8
10
38
2i
4
5
79
5A
6A
8A
loi
39
2A
4A
5l
80
5J
8A
loi
40
.2|
4A
5i
81
5A
6H
^xV
lof
41
2H
3A
4A
5i
82
s\
7
8A
loj
42
2|
3A
4A
5^
83
5A
7A
8A
lof
43
2II
3A
4A
5f
84
5I
7A
8A
lof
44
2|
4A
5f
85
5A
7A
8A
loi
45
2H
3tI
4tV
sl
86
5i
7A
8A
II
46
3
4
4A
6
87
5A
7A
8A
Hi
47
3tV
4A
4A
6i
88
^K
7V
9,
II4
48
3i
4A
5
6i
89
5H
7xV
9A
Ilf
II2
49
3tV
4A
5A
6|
90
5f
7A
9A
50
3i
4x^2
5A
6i
91
5if
7A
9x'o
Ilf
no
GEARING
Table for Turning and Cutting Gear Blanks
FOR standard length TOOTH
Pitch
16
12
10
8
Pitch
16
12
10
8
Depth
of Tooth
•135
.180
.216
.270
Depth
of Tooth
•135
.180
.216
.270
No. of
Teeth
* Outside Diameter
No. of
Teeth
Outside Diameter
92
5f,
7^1
9A
llf
^33
8A
11^
I3to
i6|
93
sH
7-h
9t%
ll|
134
^K
IIT2
i3to
17
94
6
8
91?
12
135
8t\
IlT^¥
i3tV
i7i
95
6tV
8t\
9t'o
I2i-
136
8f
iiti
i3to
174
96
6J
8t\
9A
I2J
137
8-*
IIT2
i3to
17!
97
6t\
8A
9tV
I2|
138
8f
IIT2
14
i7i
98
6i
8t\
10
I2|
139
8-1
IIT2
i4xV
i7f
99
6t6
8tV
iotV
I2|
140
8h
lilt
i4x'o
17I
100
6|
8A
iot^
I2|
141
8i*
Ilii
1 4x7
17I
lOI
6tV
81^2
iot%
I2|
142
9,
'^,
14x^0
18
102
6i
8A
iot%
13
143
9tV
I2tV
i4x'o
i8|
103
6t\
8t\
iot^o
i3i
144
9i
I2A
14x7
1 81
104
6|
8it
loA
i3i
145
9t^.
I2A
i4xV
i8|
105
6H
8H
iotV
i3f
146
9i
I2t%
i4xV
i8i
106
6;
9
lOxV
i3i
147
9t6
I2fV
I4x%
i8f
107
6-1
9t\
lo/o
i3t
148
9f
I2A
15
i8|
108
61
9t\
II
13!
149
9t's
I2tV
i5tV
i8|
109
6H
9fV
iitV
13I
150
9i
I2A
i5t^o
19
no
9t\
IIA
14
151
9t\
I2A
i5i%
i9i
III
7tV
9t\
IIT%
i4i
152
9l
I2II
15/0
i9i
112
7J
9t\
IIT%
ui
153
9H
I2ii
i5tV
i9t
113
7tV
9tV
IlT%
I4|
154
9-
13
i5to
i9i
114
7i
9t\
IlT^O
142
155
9x1
i3tV
i5to
i9f
115
7tV
9t%
iitV
I4f
156
9I
i3t2
i5to
19!
116
71
9if
IIT^^
I4f
157
9H
i3t^2
i5to
19I
117
7tV
9ii
IIT%
14I
158
10
i3i\
16
20
118
7J
10
12
15
159
iotV
i3t2
i6xV
20i
119
7f6
iotV
I2tV
i5i
160
lol
i3t%
16x^0
20i
120
7 '
IOt\
J2^
i5i
161
loA
i3tV
i6x%
20|
121
7-i
I0T2
12^
i5i
162
loi
i3tV
i6t%
20^
122
I0T2
I2t%
15^
163
I0T6
i3t\
i6x^^
20f
123
7-1
loj'a
12^
15I
164
io|
i3tI
i6x%
20f
124
iot%
I2tV
i5f
165
I0T6
13H
i6xV
20J
125
7I1
I0T2
I2to
i5i
166
loi
14
i6xV
21
126
8
iot\
I2tV
16
167
I0T6
14x1
16x^0
21J
127
8tV
IOt'2
12X^0
i6i
168
lof
i4x\
17
2ii
128
8|
loll
13
i6i
169
loH
i4xV
1 7 1^0
2lf
129
8tV
loH
i3tV
i6f
170
I of
I4t2
i7t%
21^
130
81
II
i3t%
i6i
171
iotI
14A
1717
2I|
131
8tV
iitV
i3t%
1 61
172
io|
14A
i7to
2lf
132
8f
IIT^^
^3t\
i6f
173
loH
I4tV
i7t7
2l|
PITCH DIAMETERS OF GEARS
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ir>0>oOioO'oO»oO>DOw-)0»oOmO>oO>o
00 O w N ro ii-)vO t^oo O w N CO lOO t^OO O w N ro
MNNNNNNNNtOtOCOfOC^COfOcO^'t^r}-
o d
lOOOO O w coioOOO q w roioOOO O w to »/^\0 00
N N N corOfOtCroco-<t44444»OuiloiO>i^iO
„,d
corotofoco44444>o>ojoio lovo vd vd ^ ^ ri
OO
Tfd
'"°N°1C8^°'^°N°'^°N°"^°N°'^
tO'^rt-Tj-'^ioiovo lOvO vO ^O vO t- t^ t^ t^oO 00 00 00
t
O fO^ O c^vo O c^O O fOvO O cO^O O coo O COO
lo >o io\d \d vD t^ t>. t^od o6o6d>d>d>dddwMM
8^cgS.8 8^c§8.8 8^<g8v8 8^^g^8
\o o vd t^ riod o6o6d>d>ddd WW NCNcscoco'j-
N M
a8s>8s>8a8s,8s>8a8a82>8a8a
r-oo oOOOOOwHNNcoco'd-'l-io >ovO O t^ r-
t
"?f
OO coOO fOQO roOO fOQO fOOO roOO <0
OO coOO coOO coOO coOO cOOO coOO CO
OO "?qo t^qo foqo ^700 '^ O'O^ '?9'~*^ '?
ddwNNco44 wio 0 r^ 06 codvdo'wcsNfO
H :::::::::::::::::::: :
3 too r-od 6v d w N CO 4 »oo t^od d> d w n co 4 >o
r^HMHHHNNNNNNNNNNCOCOCOC^tOCO
112
GEARING
§2
ir)OioOioOioOv50>oO»oO»oOi^O"^0>/^0>nO>JOOi/50 »oO
^00O>C^00MM(^lM^0^0'*^lO loO O r- J--00 00OvaoOMM<NNto
•Ml-IH(SC-)CSC»P)NNNMNMMNe)C<«<SMWMrOfOfOcO'0<'>t'>
^6
tr, M r-roOO «00 xow t^foOO <N00 »J^M t^foOO c^M id w IC Jo O >0 «
o) CO t^ -^ »o io\0 O r^oo 000>OOMw«rotO'=l->o lOvO O r^OO 00 O^ O O w
'I-
M C) -:j- ID 1^00 O M tS ■* lO t^OO O M P) -^ ID t^OO O H CS ■>:J- >D t^OO 0 W « '^
f-^MOC10<NOr-^MOOVri(SOt^-+H001D<NOt^^lHOOtDOl5t^'<tw
iDvO t-~ t^oo O»00iHMCsro"*'D >o^ t^ r^oo OOOw'NPirO'^io loO t^
<N oi oi M C) M coro^0rO^0tOcocor^ro^0COfO<r)444444444-<t4
00
M 6
O fOvO O fOO O coO O fC^O O wK3 0 fO^ O ^0^ O f^O O fOO O fDvO o
goo r-lOrOM OCOvO idcOm OoO t-lDcOw OOOO lOrO" OOO I-.1DOM O
q O I-; CJ t<0 "^ lo LOO f^co OOOmojco^io idvO r^oo 0>OOM<NrOT)-io
2?
O t^oo «> q H 0) CO rj- loo r-.00 O 0 M <N CO Ti- iDvO f^oo 0> O H « co ■* >«\0
coco«r)co444444'<t444>D>o>oiDiAiD>oio»o xoo vd >d vd vd <5 ^o
00 6
OuDOioO»oO>DO'>^OiDO>DOtDOioO>J->OiDO>DQtDO>DOiDO
OofiDr^ONtot^OtNior^Ocsiot^OcsiDt— OP)iot^Oo)V5r-Ocs>D
uio r-.00 O H cj CO loO t-.00 6 w c^ CO mO t^oO O w Pi co >D\0 r-OO q w «
4444>o>oioiAiDiAir) iD-d \dvd>d^\d\dvd r^t^i^tir^i^t^ t^oo 06 00
vo d
00 cog^O coQ'O coO'O COOVO coOvO coQvO coQvO coOvO cOq^ '^O
8^ ;?a^^8^ ^a^,^8^ ^^.^SS^^, 5:?S.S^8^ ^°,^S2
\6<i<i^'6<i t^t^t^t^r-t^ooodoocoodco d d & 6^ d d 6 6 6 d 0 d m
too
8 ^^^ 8 S %S^_ 8 S ^^^ 8 8 ^v8=§ 8 8 ^^<g 8 8 ^.8^ 8 8
r^ t>. ri t^oo o6o6o6oddid^d>did>dddddw'-iwHMNcio)cJ«coco
oo
Q>DO»DOiDOiDO>DOioOvoO>DOtoOiDQ>^0>DOtoO>DOioO
Ow>Dr^O<^'>Dt^Oc^'Or»OC)ii->t^Oou->t^Oc^'Dt>-0"'Dr-.0«»o
ddddd d d d m m w m o< <n <n <s t^ror^^-^-^^'t"^^^ "-jo vd >d
CO M
§ S§ § SI § SI § 31 § SI § SI 8 SI 8 SI § SI 8 31 8
pi p) pi cor.^co'^-t^iDiD >A\d vd 'd r~ t^ r-o6 oooddvdvdvddoMMHM
^cg 8^ 8 ^-5 8^ 8 ^^ 85 8 ^^ 85 8 ^c8 85 8 ^5 85 8 ^
^ ri- lo »DvO >0 <5 r- t-=0 «00C^C^00OwMPlP^Plcoco^Tl-T)■^D iDO vO
M M
8a8a8a8a8s>8a8s.8a8a8s>8a8s>8a8a8a8
00000>0>OOi-iMPfP<cocO'*tiD too O t-- t~-00 00»O\O0M>-iP)P<fO
>o O
oo ^OvD coOO coOO '^O^ coOO ^OO COQM3 c^OO f^Og coO
4 4 >D>d vd t^oo oddddw<^pico44 ^^ ^ «>•!» o6d>ddMpipico4
P< P< <N p» N « P> P) « cocClcOfOcococococOfOcOcocOPncO'*'*'<t^'<t-s»-rl-
^ ::::::::::::::::::;::::::::::: :
PITCH DIAMETERS OF GEARS
113
sS
Ir)0>o0>^0»o0io0»o0io0io0»ri0>n0»n0>o0»^0>/I0»o0»o0>o
00 lOM t-fOOvO <NO0 mM t-.c/560 MOO iOM ts-fOOWD <S00 >ir>M t-roOO NOO
M <N to fO ^ "p iip>0 vq t^oo oOOvOOHMMfOro^io upvq ^ t^OO 00 O' 0 0 m m
^6
VOt-OO 0 W M ^U-)t^cO 0 M (N -tri^t^OO OHM '+lOt-.00 Q M M rHo f^OO 0 M
00>0<NOI--^>-(OOlOMOt-^WC010MOt-^MOOinMOt--*MOO >0 M O t^
t>-oq o^oOMMMfO'+to 100 t- t--co c>oqi-iMCNco^io 100 r- 1^00 000
444iou^'toiniAioioioi/^ir>toioio vovd oovdvdvdvd^doo^d-o^vd i^i>-
00
M d
too 0 ^0^0 0 fO^ 0 c/50 0 "OVO 0 "OVO 0 c^O 0 fOvO O r^O O r0>0 O N^\a O
c^oioroMOoor-i^cowOooOintOHOoor-xocoMOoovoio ro m 0 x'F. ih
ir;^ t^oo qoq>-;M^^"7 "jp^ t--oo qoOMMr^'+io liovq t^co a 0 0 « m
lA lA in vo lovd oMSvd^JOOvd^vdvdo t^i>.rii<.t>.r^t^t^t4t4t^ riod oc 00 06
2I
t^co q 0 H M ^ ^ 190 t-.co q q H M CO ■* lovq t^oo q q >-; <^ ^ -+ v~,\o r-oo o>
vdo^ t-lr^t^t^(>.t^r^t^t>. t^od cdcdodooooodododod d>d^ dv_d> c< dv d' d> dv d^
CO d
ir, 0»nOioOi>^OiJig>nOioqioO'00>r>0>J^OioO>nOioOioO>/^Oi/1
r^OMinr^OMiot-OMior^OMu^t^OMiot^OMiot^OMiof-OMior-.
cc 100 r-OO 0 w M <^ if^.O t-.CO q M M -0 vr,0 t-~CC q w m ro VOO t^oO O h M ro
ooodooocoodd^dd-ddddddddddddMHHMHwwwoioJMM
-o d
vO rOOvO fOOO rOOO ^OOO roOVD fOOO fOOvO r^OvO <r>00 rCO<5 -OO
vO fOOO ro 00 rOOO roOO rOOO fOOvO roOO rOOO fOOO fOOO r^O
M <v-, upvq 00 q M CO upvq <» q h to too co q m co »o^5 co q « co iovo 00 0 « -^ Co
H w H w M M M M M M oj COCOCOcOCOCO-:t-44444>OlO>OlOl/^ l>-,VO O vO MS
lod
^^cg 8 S ^v§^ 8 S ^^^ 8 S ^^<g 8 S ^^^ 8 S ^^^ 8 8 ^S^
coco'o4't444wioio>o >o\d vdvdvdvd r^t>.t^t^ r-^od ododoooo' d d 6^ d d
00
^d
;c8^9,ic8^s>ic8J?ajc8J?a:c8^s>ie8^aie8i?as8i?aie
^ tr ^ ^ ^ ^ ^ ^ ^ ^ ? 2^ ? s S S 8 ^ j:i ^ ^ 5^ ^ ?i ^ ^ 5? ?? J? jf ^ ^ d"
C0~0 0 COO 0 <00 0 COVO 0 cOMD 0 COO 0 COO O COO O coO O coO O COO O
COO 0 COO 0 COO 0 COO g COO 0 COO 0 COO 5 fooo coo 0 coo 5 coo 0
coo 0 coo 0 covD 0 coo O coO O coO O coO O COO O cOO O coO Q coO 0
M M c5coco444ioio lAo vd o f-^ f^ r^oo oocdddddddMMMMrJMco
NMMMMMMMMMMMMMMMMMMMMMMCOCOCOCOtOcOCOCOCOCO
eg Sv8 8 ^.g 8v8 8 ^<g Svg 8 ^<g 8^ 8 ^<g S^g 8 ^<g S.8 8 |c§ 8vg
o t^ 1-^00 ododdvdvddoMiHMMMcofO'^'i-'*!') »oo o o t~- t-^oo od od dv di
M M M M M M M M tOfOfO<OfOtOco^OcOcOtOcO^OcOtOcocOcOc0^0cO^OcocOfO
S>89>82,8a8a8a8S>8S>89>8 9-.82,8a8a8S>8a8a8a
CO ■* "* >o loO O r^ r^c« cdodiddi-i>-iMcicoco-^-T>o vovo O r-^ t-^od od o d>
ro«:i'OCOcOco^"^'OCOCOcOcOrJ--*rtTi--,j-^Tj-Tl--C'3-Ttrt'^'t-*^'*-*'<j-'<l-'
.!
o cogo cogo cogo cooojooo cooo cooo cooo cooo cooo coo
o cooo cooo cooo coootooo cooo cooo cooo cooo cogo coo
tj- lovd vd t^od oddvddwMMfo^'ct u-o o t-^cd odd>doMM'Mco-*-4- »A,o
■^t'*r)-T)-^^-T>0>ouii/->ioioio>oioiou-)ioioio iTiO OOOOOOOOO
QCJ
^ ::::::::::::::: i : M :: i ;: i : M :::: i
114
GEARING
u-;iiiuiiOii^»jSioio«0'Oioin\oir)ioioi/>iOio ICO vd\Osd^\d<)>Ovd
ly^M t^foOvO <NO0 lOM t^?oQO (NC«inH tCJoOO c?<» 10 w IC Jo 8
<N ro fO ■* >o "^vO 0 t-e» oOOvOOwMNrOro-^l-i/i lovo vO r-OO 00 0> O
vdo^vd>0^o'vdvdv6vd^ t^r^r^t^t^r^i^Ltit^t^t^tir^t^t^ t^oo
J
?d
N T}-»/>t^00 0 M N TfV5t^00 0 M M 'tiJit^oo Own rf m t^oo O h N
TtMCO ION Ot^-*WCOlON Ot^-<tMOO»ON OJ^-*MOOVON Ot^"*
M N N ro -^ »o vovO i~~ r^oo OiOOmnnco-^io lOO t^ f^OO 0> O O w
t^t^r^t^j^t^i-^rCtC.t>r^ t^oo.oo 06 06 dod ooododododododoo 6d>6
00
2d
ooooocjododoooooo 6'6'0><><^0'0'0'<^<>0'<^0 6 6 6 6 6 6 6 6
2I
O M N fo rj- \n\o t~.00 O O w N <<5 <t lovo t^OO Oi O H N fO •* tOO r-00
00?
0>o0io0io0»o0>o0to0»o0>oov>0>o0>o0to0io0^0
ONiot>-ON»or^ON»or^ONinr^ONint^ONu-ir^ONiot^O
»Ovo r-oq O M N ro to\q r~-00 O M N CO lo^ t-.00 O m n ro lovo t^oO O
N N N N co^orO^0fOrC^^fr>4't444444l^^O>O>J^lO^OlO ir>\6
vo 6
vO lOQvO r^OO toOO f^OO tOQO rOOO <nOO fOOO tOOvO fO
VO rOOO roOO foOO rOOO "^OO roOO fOO'O pOOO rOOO rO
ooo q M coi>)vqoo q w ovoooo q m tolovqoo O -- toinooo O M CO
vo vo ri t^ !>. ti t^ t^od ododododoo d>6vc>6v6>dd d d d d d « m w
00
lod
8 g ^^^ 8 S ^^cg 8 S ^^cg 8 S ^^cg 8 8 ^^cg 8 S ^S
dddddMMWM>-.NNNNNrocorOfOff>4't4-*-*»oir)>oio
NNNNNNNNNNNNNNNNNNNNNNNNNNNNN
10
00
■*d
0>oOinOtoO>oQ»no<oO»oO»oO>oO>oO»oOioOioOioO
ONlOt^ONlOt-ONlOt^ONlOt^ONlOt^ONinr-ONlOt^O
ic lo lo lio^d vd vd \d t^ t^ i^ i^od odododdvddvdvdd ddMMMMN
NNNNNNNNNNNNNNNNNNNNfOfOCOfOCOCO^OeOrO
COO O fOO O f<^vO O rovO O r0>0 O fO<0 O COVO O ^0^O O f^vO O fC>0
POO O POO O OO O fOO O fOO O fOO o ^oo o coo O coo O coo
coo q coo q coo q coo q coo o coo o coo o coo o coo o coo
CO CO 4 4 4 -o >A uio o o t^ t^ r^od ododdvdvd<ddd wwmnnn
rOcococococococococococococOcococOcocOcOTl-^Tl-Tt-^Tl-Tt'^'t
ION
pj M
8 ^cg S^ 8 ^cg S^ 8 ^^ 85 8 %& 85 8 ^^ 85 8 ^cg 8
OOOMMNNN^^^^^^^OOO^^odcdodddddOM
M H
8a89,8S,89,8a8a8a8S>89>8a8S>8a8a8a8
ddwi-'NN'oco^'tiA loo o 1^ t>-od odd>d>ddw>-<csp)coco4
iotOLoLoioioioioiovo>oir>>oioio>oioioi>) iho O O O O loo O O
-1
M C4
O COOO COOO COOO coOO COOO COOO coOO COOO COOO CO
H :::::::::::::::::::::::::::: :
iSssssslsssSHHSSH^H'SSsHHsJssEs
GEAR CUTTERS AND CUTTING
IIS
B. & S. INVOLUTE GEAR TOOTH CUTTERS
No. I will cut wheels from :
No. 1 1 will cut wheels from
No. 2 will cut wheels from
No. 27 will cut wheels from
No. 3 will cut wheels from
No. 3i will cut wheels from
No. 4 will cut wheels from
No. 45 will cut wheels from
No. 5 will cut wheels from
No. Si will cut wheels from
No. 6 will cut wheels from
No. 65 will cut wheels from
No. 7 will cut wheels from
No. 7i will cut wheels from
No. 8 will cut wheels from
35 teeth to a rack.
80 teeth to 134 teeth.
55 teeth to 134 teeth.
42 teeth to
35 teeth to
30 teeth to
26 teeth to
23 teeth to
21 teeth to
19 teeth to
17 teeth to
15 teeth to
14 teeth to
13 teeth to
12 teeth to
54 teeth.
54 teeth.
34 teeth.
34 teeth.
25 teeth.
25 teeth.
20 teeth.
20 teeth.
16 teeth.
16 teeth.
14 teeth.
13 teeth.
The eight cutters represented by the whole numbers constitute the
regular set of cutters generally used for each pitch of tooth. The
half numbers increase the set to 15 and gives teeth which are theoret-
ically more correct. In some work special cutters are used for each
gear but the 15 cutters in a set offer all that most cases require.
Table Showing Depth of Space and Thickness of Tooth
IN Spur Wheels, when cut with these Cutters
Pitch
Depth to be
Thickness of
Pitch
Depth to be
Thickness of
of
cut in Gear
Tooth at Pitch
of
cut in Gear
Tooth at Pitch
Cutter
Inches
Line. Inches
Cutter
Inches
Line. Inches
li
1.726
1^257
II
.196
•143
i^
1.438
1.047
12
.180
• 131
If
1.233
.898
14
• 154
.112
2
1.078
.785
16
• 13s
.098
2-
.958
.697
18
.120
.087
2-
.863
.628
20
.108
.079
2?
.784
.570
22
.098
.071
3
.719'
•523
24
.090
.065
3h
.616
•448
26
.083
.060
4
•539
•393
28
.077
.056
5
.431
.314
30
.072
.052
6
•359
.262
32
.067
.049
7
• 308
.224
36
.060
•044
8
.270
.196
40
.054
.039
9
.240
•175
48
•045
•033
10
.216
.157
BLOCK INDEXING IN CUTTING GEAR TEETH
Block or intermittent indexing is a method to increase the output
of gear cutters by allowing the feed and cutting speed to be increased
without unduly heating the work. This is done by jumping from
the tooth just cut to a tooth far enough away to escape the local
heating and on the following rounds to cut the intermediate teeth.
While the indexing takes a trifle more time, the heat is distributed so
that faster cutting can be done without heating and dulHng the cutter.
The following table gives the indexing of gears from 25 to 200
teeth and is worked out for the Brown & Sharpe gear cutter but can
be modified to suit other machines.
ii6
GEARING
DsiQ SatiiooT JO sumx
NNNNMN<NN(NNNNNIN«WNMMNO)N(Sf)NN ,1
i3Monoj pnoD3s 1%^^^^"^^^^%?-^ 9,^^z^^ S;^^^=5^^;g ^
aaAUQ pncoas [ ^ o? go? g 8^cg go?^ g RS g S.^°^ gcg <;? goj g Re?
a9Mono J isiij 1 R ^ ^ g,^ S!. g, ^^ ^ S,5 -S ^5 g.vg ?v8 v8 ^S 5,S S^S
J3AUQ }SJl j^
22§2§^2°2§2 22^22222222222^
30UQ XB paxapUJ 'O^ | u^ l> >o i> ^O t^irim t^oo >i^ r^ 0> »o<o r~ioiovoJ--iot^ior~l^ ||
in3 aq o; q^aa^
>O<5OOvCOr^t-r^i>r^t^000000000000C000 0>OvO>0>OvO
DSJQ 3ui:5[DOq^ JO SUJTIJL |f)<NMNCINM<S(NN(NNNNMMMNNNeiN<N<NlNNN
jaMonoj pnoDas |:2 ^ S, ^^g ^ ^^v^ 5;§ ^ R ^ J?> R^ ^ S S>^5 S ^ '^.J
ja.vuQ paoaas o? go? S, go^c^cg ^ g^ gc§ gcg ~g g Reg g^ g<g R R go?
jaMonoj isjij 1 a o o o o o o go o o o o « o 50 2 0 « 0 0 0 g ^o 00 0
javUQ JSJTJ
2222§22222222°§S.88888888888
aaUQ 1^ paxapuj -O^ |t-iot^io>ot-t-io^«Jit^>oioro ^J^^O >/^0 u^ u^ r^ lo u~, VO.O 10 r-| 1
;n3 aq 01 qpax
CO'^IOOOO OO N c^TMovOOO O w ro-^i^t^oo O M fO tT »ovo 0
asiQ Sni-5tao'j[ jo snjnx I<n(n(s<n<n<n<nnmn(nnoi(m(nn(n(nn<nmnnnp)nn
jaMonoj pnoaas \^%^ ^^^^ §;^^^ ? ^S 2>5 5 ? ^^^^'S^'Rg ^ ?
aaAUQ puoaas | go? g R R g^ g^ g g^ ^S gS R^cg g.J?^ g^ R R^
aaMonojjsiH|oooooooooooooooooo;tooooooov^
aaAUQ jsjTj
88888888888888888888888888^
aauQ ^B paxapuj "O^ |u^i-iot^ro>ot~.ir;-<tioio2 i^"^iott>t->A>»/^ t-00 >^oo c^ f- ttI
jn3 aq o; q;aax
O r~oO O M P) fO ■Tf i/ivO 00 0> O <M t ''lOO O m N ■^ >o\0 r~ Cv O w
000000O>OvO>aOvOvOvO>O>OOOOO>-iwi-iMMMMMNN
aSIQ SUI-JIDOI JO SUjnX |w<NNN(N(NNN<NNN<NNaM<N<NtN<NP»««Pt(NN(NN
aaMO„o J pnoaas | ^ 5 ?^^^ ^^ ^^ J?, ^^S ^ R R R S.^ ?^^ J?,^ o?§
aaAUQ puoaas | g g^ g^ go? gcg g^cg g gcg g g go? g^ g g^ g g^
jaAVonoj;s.H|o 00 0000 000 0500^0 00 00000 00
jaAUQ ISJIJ
888888888888888888888888888
aaUO J^ paxapUI •OJsl|i/-,.y^TM/l^^r-.r>./^,./^^.^uiv,.oro.o.r>l-.r,^,oror-.o.ort
■^nj aq o; qjaax |ii^ir)ioioi/-, u-;0-ovoovovovo>o<5 t-r-t-r-t-r- t-oo oo oo oo oo
asiQ SnT-5[aoq; jo suanx l^^'^'^'tiN Tj-^TrTrfr'^-*^^-*T}-Ti-^-*'*Tj-n-^Tr<s
jaAvono J puoaas | ^ ^ ^^'^S ^ ^ ?g ^ ^ R^^cg cS o?g §8 ?> S. S^^g ^S
jaAuapnoaas | R g^ g gv8 g g^ g^.g g g g g g g g gR g g g go?^
jaMonojJsai^ aaaaaaaS>g>S>S>°^?=a?=a3.^3>^a3.?>?>?.aa
jaAUQ ISJIJ
888888888888888888888888888
M M M M M M
aaUQ IB paxapuj 'O^ \ rt n ^ flton rofOTtrO'<t>^>^>^>>^fOiouiu-)>ilt^i/^iA>o»ot^'*|
mo aq oj tpaax
|{?^?r^^g>sif^??S}?^J:?^^^^^??^^$<^5S>c,|i
DIMENSIONS OF GEARS BY METRIC PITCH n?
THE DIMENSIONS OF GEARS BY METRIC PITCH
Module is the pitch diameter in mm. divided by the number of
teeth in the gear.
Pitch diameter in mm. is the Module muhipHed by the number
of teeth in the gear.
M = Module.
D' == The pitch diameter of gear.
D = The whole diameter of gear.
N = The number of teeth in gear.
D" = The working depth of teeth.
t = Thickness of teeth on pitch line.
/ = Amount added to depth for clearance;
Then
M = — or r— - — ,
N N + 2
D' = N M.
D = {N + 2) M. ^\ \>-
^T D' D
D" = 2 M.
t = M 1.5708.
M 1.5708
/ =
= .157 ^'
The Module is equal to the part marked "S" in cut, measured
in mm. and parts of mm.
.Example: Module = 3.50 mm. 100 teeth.
Pitch diameter = 3.5 X 100 = 350 mm.
Whole diameter = (100 + 2) X 3-5 = 357 mm.
Pitches Commonly Used — Module in Millimeters
Corresponding
Corresponding
Module
English
Module
English
Diametral Pitch
Diametral Pitch
\ mm.
50.800
4.5 mm.
5-644
1
33-867
5
5.080
I
25.400
5-5
4.618
1.25
20.320
6
4.233
1-5
16.933
7
3.628
1-75
14-514
8
3-175
2
12.700
9
2.822
2.25
11.288
10
2.540
2-5
10.160
II
2.309
2.75
9.236
12
2.117
3
8.466
14
1.814
3.5
7-257
16
1-587
4
6.350
ii8
GEARING
SPROCKET WHEELS FOR BLOCK CENTER CHAINS
N = No. of Teeth. E = ^'
C = Diameter of Round Part of
Chain Block. Tan D =
Sin. E
B
+ Cos. E
B
Center to Center of holes in Chain
Block.
A = Center to Center of holes in side
links. Pitch Diam. = — — — .
Sin.Z)
Outside Diam. = Pitch Diam. + C.
Bottom Diam. = Pitch Diam. — C.
In calculating the diameter of
•Sprocket Wheels the Bottom Diameter is the most important.
Diameter of Sprocket Wheels -
A = .6*. B = .4"
Fig. 9
FOR
c -
BLOCK CHAINS V
PITCH
No. of Teeth
Pitch Diameter
Inches
Outside Diameter
Inches
Bottom Diameter
Inches
6
1-935
2.260
1. 610
7
2.250
2.575
1.925
8
2.566
2.891
2.241
9
2.882
3.207
2-557
10
3.198
3.523
2.873
II
3.515
3.840
3.190
12
3-832
4.157
3.507
13
4.149
4.474
3.824
14
4.466
4.791
4.141
15
4.784
5.109
4.459
16
5.102
5.427
4-777
17
5.420
5.745
5-095
18
5-738
6.063
5-413
19
6.056
6.381
5.731
20
6-374
6.699
6.049
21
6.692
7.017
6.367
22
7.010
7-335
6.685
23
7.328
7-653
7.003
24
7.646
7.971
7.321
25
7.964
■ 8.289
7.639
26
8.282
8.607
7.957
27
8.600
8.925
8.275
28
8.918
9-243
8-593
29
9-237
9.562
8.912
30
9-556
9.881
9.231
DIAMETERS OF SPROCKET WHEELS
119
Calculating Diameters of
Sprocket Wheels for Roller Chains
N = Number of Teeth in Sprocket
P = Pitch of Chain
D = Diameter of Roller
. -360^
^ ~ iV
p
Pitch Diameter = —. — t—-
Sm. i A
Outside Diameter = Pitch Diameter + D
Bottom Diameter = Pitch Diameter — D
Fig. 10
Diameter of Sprocket Wheels for Roller Chains 1" pitch where
D = .45.
Diameter of Sprocket Wheels for Roller Chains of i'^ Pitch
WHEN D = .45"
No. of Teeth
Pitch Diameter
Outside Diameter
Bottom Diameter
in Inches
in Inches
in Inches
6
2-
2-45
1-55
7
2.305
2-755
1.85s
8
2.613
3-063
2.163
9
2.923
3-373
2-473
10
3-236
3.686
2.786
II
3-549
3-999
3-099
12
3.863
4-313
3-413
13
4.179.
4.629
3-729
14
4.494
4-944
4.044
IS
4.809
5-259
4-359
16
5.125
5-575
4-675
17
5-442
5.892
4-992
18
5.758
6.208
5-308
19
6.122
6.572
5.672
20
6.392
6.842
5-942
21
6.747
7.197
6.297
22
7.025
7-475
6.57s
23
7-344
7-794
6.894
24
7.661
8. Ill
7.211
25
7-979
8.429
7.529
26
8.296
8.746
7.846
27
8.614
9.064
8.164
28
8.932
9.382
8.482
29
9.249
9-699
8.799
30
9-566
10.016
9. 116
I20
GEARING
A TABLE FOR DIMENSIONS FOR MITER GEARS
_ The ^ accompanying table is of service in determining the prin-
cipal dimensions of miter gears (center angle 45 degrees), the num-
ber of teeth and the pitch being known. The table covers most of
the possible number of teeth from 12 to 60, inclusive, and pitches
from 2 to 10, inclusive, omitting 9. Values for face and cut angles
correspond with designations in Fig. 11.
't O O^ <> O 00 ■*^0>'''N vo^ tb lo '^ cs o><D^rO C^ ^ O lo 0> ^00 " o'h <N coo <N 00 ^ o
»- r-CO XOvO>OOOOOOH>HWWI-IHWMtSMMC^O)NININ<N<SC^COCOrOtO^O
rOWr^rOfOioO>iDrOM m m (n -^i—O ^r~Mt-Mr~.coO>tDMCO wO OO O) t--i-i ^^m
°M °H °0 °0 °0 °0\°0°a°OvoO 00 CO 00 CO 00 00 W°r>. W W W WVvO \o o^o o o >o O
6
s
0
a.'
00
PO Tf u-,o t^oo 0>0 " M rOrTLTiO r;- iO 0> 0 "^ <^ ^O -f lt-O r-;-CO 0-; rOlAr^q^M loCvi-
H H M M w iH w cs o5 C4 pS ci M N ci N N rorOrOfOfOrOtOrOrorO'^'<i-'<t'^'1">0»OiOvC
00 w COO 00 H roOOO M roOOO w roOoO m <00 00 m 2"° °9 J;! ^^ 2°9 J?=° 2 J? 12^
ooo o o " to ^ 1/1O00 oo w fo'twpooo oq « to-<ti^ooq q.^^ 'to cvw ■^ q^rf^_
H M M cj N N <N e5 M ci ci cotototofororo<o44'i-44444'oin>oioooor^t^
^
c^
M M N ci M « M ci tOtotOcorOtOfo444444'i->OiOiAiAiO i^-o O O t^ t^ t^CO CO
^ JN ci ci c5 cj totOfOr^tot^444444>n>oiOioio lOO o >0 >0 O t^ t- t^oo CO Ov O 0
0
0
z
<;
i
z
Ch 1 f^-o^s " rovo DO « too 00 -; <^ooq 1^ ^<?«5 '-'. f^^^O "^ '^^^^ fOM roco cooqoqoq ro
^ ic<Sco'^'t444'OiO»A lOO ^ O <5 r^ t^ t^ t^OO odcXDOO O'dc^O^O O m w n w ^2'm
a: h& ?^5 ?°^5 ?^cg ^'^;2 ^^=g ^°^cg ?^c8 r^cg ?cg°T?«^^°|cg^
^ i 44>o>oiooovd t^t^ r^oo'odoo 6\6>6>d66"H«<Nfi<N'o^4|o »oo t^oo a o
<
w
0
Ci^
^I.Nii«r^N^.N^i«ttMtiwtiN^^Nr-Nt--Nt-N^-Nr^^-t-t-t^r-t^^-.^-^^
on
H
o t^ «>o6 o66»ovddwn<NNtoto44»o »^o o t^ t^oo oc5 o>dvp « n JJ^JJ^^'gj
a
.2
Q
o
«2"2-2'»2«2'-2»2=S -^"2-2-2-2-2-2x2-5 -2-2-'2-2-2-2^-2-2 «2^2»S-2 -2^
MHMMMHl-IMNCJMNNNMNCIMtorOtOtOtorOtOtOtO'^'^'^TrrH/llO >00
CO
7;1? M^? N N pT c?^^ N « tot^toti^totocoto't^^'T'^^'tioio.o.oooor-t-
Oh*
io»-ot- r«--<»-n>'*t-iot-sa» -.■(-tw-^,>-«t-ct-;t- -a^Nt-nt-att-ol-c*- --!b.^>l-r>«-c^^ oi— i^-cv- ■»-i5»-t»»-«-
1-1 p-l N n'm M N P) P) fOtotOtOtOtOtO't'^t'l-'t'^ttOlOVOlO w-)0 o O O t- t-CO 00
a^ M cT <N « N (N toTo fOrorO^^^TrTr^■^^^lr)»ow^tol/^ lOO vO O O r- r- 1-00 CO O. O. 0
>o 1
Oh 'n" pi m fo"^ 'O rOtO'^'*'^'*'*'') "1 >0 lO voo O O O »0 t- t> l— t--X 00C0O>O>OO'-iN
to'co'to'^ t ■*'^'^ >o W-) lo'ioo o o'o i-» 1- r- t-oo oooocb oao\o 6 « « « « totw
MM M
fo
-«r*9 HMNiw -*?c*5 H?;c<<n Hretitn .H«t*o -<nf*o .-i»c*o r^reM|n-<« r*i-»n '*'.'*?_
rj- ^ Tf >/l »0 »00 O O t- t- t~-00 00Q0C^C^C^0OOMwwP^WNto■*t i/^O o oo a 0
MMMMMMMMM
O o" t-'SoO OOO-^O O w w'w P)"cotOt't>0 loO Ot-t^00o6 OiO M w "''^ijfr^?!
M M W M M M
}0
33X
•ON
2 22-;?^j:<s?8 5SJ??jr^j:^g'^siS!.J?;sj^^f:^%^^?^^a;^^^
BEVEL GEARS
121
Fig. II, — Bevel Gear Parts
BEVEL GEARS
Bevel Gears are used to transmit power when shafts are not par-
allel. They can be made for any angle, but are more often at right
angles than any other. Right angle bevel gears are often called miter
gears. The teeth are or should be radial so that they are longer at the
outer end. The names of parts are sho\ATi in Fig. ii. These should
be noted carefully, particularly the face angles. The earlier editions
measured /oce angle at right angles to the axis, but this is now changed
as shown.
LAYING OUT BEVEL GEAR BLANKS
In laying out bevel gears, first decide upon the pitch, and draw
the center lines B B and C C, intersecting at right angles at A as shown
in Fig. 12. Then draw the lines D D to E E the same distance each
Fig. 12. — Laying out Bevel Geaib
122
GEARING
side oi B B and parallel to it; the distance from D D to E E being
as many eighths of an inch — if it be 8 pitch — as there are to be
teeth in the gear. In the example the number of teeth is 24; there-
fore the distance from D D to E E will be \*-, or i| inches each side
oi B B. K K and L L are similarly drawn, but there being only
16 teeth in the small gear, the distance from K K to L L will be -^/,
or I inch each side of C C. Then through the intersections oi D D
and L L, E E and L L, and E E and K K, draw the diagonals F A.
These are the pitch lines. Through the same point draw lines as
G G at right angles to the pitch lines, forming the backs of the teeth.
On these lines lay off | of an inch each side of the pitch lines, and
draw M A and N A, forming the faces and bottoms of the teeth.
The lines H H are drawn parallel to G G, the distance between them
being the width of the face.
The face of the larger gear should be turned to the lines M A , and
the small gear to iV ^ . For other pitches the same rules apply. If
4 pitch, use 4ths instead of 8ths; if 3 pitch, 3ds, and so on.
Bevel gears should always be turned to the exact diameters and
angles of the drawings and the teeth cut at the correct angle.
NG'No. of Teeth in Gear
NP=No. of Teeth in Pinion
CG = Center Angle of Gear
CP= Center Angle of Pinion
Fig. 13. — Finding the Cutter to Use
Proportions of Miter and Bevel Gears
To Find the Pitch or Center Angle:
Divide the number of teeth in the gear by the number of teeth in
the pinion. This gives the tangent of the pitch angle of the gear.
Or divide the number of teeth in the pinion by the teeth in the gear
and get the tangent of the pitch angle of the pinion. Subtracting
either pitch angle from 90 gives the pitch angle of the other.
CUTTERS FOR BEVEL GEARS 123
To Find the Outside Diameter:
Multiply the cosine of the pitch angle by twice the addendum
and add the pitch diameter.
To Find the Outside Cone Radius or Apex Distance:
Multiply the secant of the pitch angle of the pinion by ^ the pitch
diameter of the gear.
To Find the Face and Cutting Angles:
Divide the addendum by the outside cone radius or apex distance..
This gives the tangent of the addendum or outside angle. Subtract
this angle from the pitch angle of the pinion to obtain the cutting
angle of the pinion, and the face angle of the gear. Subtract the
same addendum angle from the center angle of the gear to obtain
the cutting angle of the gear and the face angle of the pinion. This
gives a uniform clearance and is especially for use with rotary cutters.
To Find Hight of Addendum at Small End of Tooth:
Divide the addendum at the large end of the tooth by the outside
cone radius. This gives the decrease in hight of the addendum for
each inch of gear face. Multiply this by the length of the gear face
and subtract the result from the addendum of the large end of the
tooth. The difference is the hight of the addendum at the small
end of the tooth.
CUTTERS FOR BEVEL GEARS
Lay out the bevel gears and draw lines A and B at right angles
to the center angle line. Extend this to the center lines and meas-
ure A and B. The distance A = the radius of a spur gear of the
same pitch, and finding the number of teeth in such a gear we have
the right cutter for the bevel gear in question. Calling the gears
8 pitch and the distance A = 4 inches. Then 2 X 4 X 8 = 64
teeth, so that a No. 2 cutter is the one to use. For the pinion, if B
is 2 inches, then 2X2X8 = 32 or a No. 4 cutter is the one to
use.
124 GEARING
USING THE BEVEL GEAR TABLE
Take a pair of bevel gears 24 and 72 teeth, 8 diametral pitch.
Divide the pinion by the gear — 24 -^ 72 = .3333. This is the tan-
gent of the center angle of pinion. Look in the seven columns under
center angles for the nearest number to this. The nearest is .3346
in the center column, as all these are decimals to four places. Fol-
low this out to the left and find 18 in the center angle column. As
the .3346 is in the column marked .50 the center angle of the pinion
is 18.50 degrees. Looking to the right under center angles for gears
find 71 and add the .50 making the gear angle 71.50 degrees. Thus:
Center angle of pinion 18.5 degrees.
Center angle of gear 71.5 degrees.
In the first column opposite 18 is 36. Divide this bj^ the number
of teeth in the pinion, 24, and get 1.5 degrees. This is the angle
increase for this pair of gears, and is the amount to be added to the
center angle to get the face angle and to be deducted to get the cut
angles. This gives
Pinion center angle 18.5 + 1.5 = 20 degrees face angle.
Pinion center angle 18.5 — 1.5 = 17 degrees cut angle.
Gear center angle 71.5 -f 1.5 = 73 degrees face angle.
Gear center angle 71.5 — 1.5 = 70 degrees cut angle.
For the outside diameter go to the column of diameter increase
and in line with 18 find 1.90. Divide this by the pitch, 8, and get
.237, which is the diameter increase for the pinion. Follow the
same line to the right and find .65 for the gear increase. Divide this
by the pitch, .8, and get .081 for gear increase. This gives
Pinion, 24 teeth, 8 pitch = 3 inches + .237 = 3.237 in. outside dia.
Gear, 72 teeth, 8 pitch = 9 inches + .081 = 9.081 in. outside dia.
To Select the Cutter
Another way of selecting the cutter is to divide the number of
teeth in the gear by the cosine of the center angle C and the answer
is the number of teeth in a spur gear from which to select the cutter.
For the pinion the process is the same except the number of teeth
in the pinion is divided by the sine of the center angle. Formula
NG NP
Tangent of CG = ^ • Tangent of CP = -^ .
NG
Number of teeth to use in selecting cutter for gear = p; — ^rr; .
Los CO
NP
Number of teeth to use in selecting cutter for pinion = -zr. — ^rp, •
Sin CG
Any pair of gears can be figured out in the same way, bearing in
mind that when finding the center angle for the gear, to read the parts
of a degree from the decimals at the bottom, and that for the pinion
they are at the top. In the example worked out the tangent came
in the center column so that it made no difference. If, however,
the tangent had been .3476 we read the pinion angle at the top, 19.17
degrees and the gear angle at the bottom, 70.83. By noting that
the sum of the two angles is 90 degrees, we can be sure we are right.
USING THE BEVEL GEAR TABLE
125
Bevel Gear Table
SHAFT angles 90°
;rj3
i, >. _
<o u
(U U
L >»
0^
< «
Center Angle
Hundredth Degrees
^1
^:2 1
c >>
S.^o
^^^
^"«
Left-hand Column read here
•- 'S
^^J
«-sl
0
c If
p5
0
.17
.33
.50
.67
•83
1.00
■S'li
I
2.00
0
.0000
.0029
.0058
.0087
.0116
.0145
•0175
89
•03
2
2
00
I
•'3175
.0204
.0233
.0262
.0291
.0320
.0349
88
.07
4
2
00
2
•0349
.0378
.0407
•0437
.0466
.0495
•0524
87
.10
6
2
00
3
.0524
•0553
.0582
.0612
.0641
.0670
.0699
86
.14
8
99
4
.0699
.0729
.0758
•0787
.0816
.0846
.0875
85
•17
10
99
5
.0875
.0904
•0934
.0963
.0992
.1022
.1051
84
.21
12
99
6
.1051
.1080
.1110
.1139
.1169
.1198
.1228
83
.24
14
98
7
.1228
.1257
.127S
.1317
.1346
.1376
.1405
82
.28
16
J
98
8
•1405
•1435
.1465
.1495
.1524
.1554
.1584
81
.31
18
I
98
9
.1584
.1614
.1644
.1673
• 1703
.1733
.1763
80
•34
20
97
10
.1763
•1793
.1823
.1853
.1883
.1914
.1944
79
22
I
96
II
.1944
.1974
.2004
.2035
•2065
•209s
.2126
78
.41
24
96
12
.2x26
.2156
.2186
.2217
•2247
,2278
•2309
77
.45
26
95
13
.2309
•2339
.2370
.2401
.2432
.2462
•2493
76
.48
28
94
14
•2493
.2524
•2555
.2586
.2617
.2648
.2679
75
.51
30
93
15
.2679
.2711
.2742
.2773
.280^
.2836
.2867
74
•55
32
92
16
.2867
.2899
.2931
.2962
.2994
.3026
•3057
73
•58
34
91
17
•3057
.3089
•3121
•3153
•318s
•3217
.3249
72
.62
36
90
18
•3249
•3281
-3314
•3346
.3378
.3411
•3443
71
.65
37
89
19
•3443
•3476
.3508
•3541
.3574
•3607
.3640
70
.68
30
88
20
.3640
•3673
.3706
•3739
.3772
•3805
.3839
•71
41
I
86
21
.3839
.3872
•3906
•3939
•3973
.4006
.4040
68
•75
43
85
22
.4040
.4074
.4108
.4142
.4176
.4210
•4245
67
.78
45
84
23
.4245
•4279
•4314
.4348
•4383
.4417
•4452
66
.81
47
^
82
24
•4452
•4487
•4522
.4557
•4592
.4628
.4663
65
.84
49
1
81
25
.4663
.4699
•4734
.4770
.4806
.4841
.4877
64
.88
50
I
79
26
.4877
•4913
•4950
.4986
.5022
.5059
•5095
63
.91
52
J
78
27
•5095
•5132
.5169
.5206
•5243
.5280
•5317
62
•93
54
I
76
28
•5317
•5354
•5392
•5430
•5467
.5505
•5543
61
•97
56
74
29
.5543
.5581
.5619
.5658
.5696
•5735
•5774
60
1. 00
57
^
73
30
.5774
.5812
.5851
•5890
•5930
•5969
.6009
59
1.03
59
I
71
31
.6009
.6048
.6088
.6128
.6168
.6208
.6249
58
1.05
61
69
32
.6249
.6289
•6330
.6371
.6412
•6453
.6494
57
1.08
63
67
33
.6494
•6536
•6577
.6619
.6661
.6703
•6745
56
I. II
64
65
34
•6745
.6787
.6830
•6873
.6916
.6959
.7002
55
1. 14
66
63
35
.7002
.7046
.7089
•7133
.7177
.7221
.7265
54
1. 17
68
61
36
.7265
•7310
•7355
.7400
•7445
•7490
•7536
53
1.20
69
59
37
.7536
.7581
.7627
•7673
•7720
.7766
•7813
52
1.23
57
38
.7813
.7860
•79='7
•7954
.8002
.8050
.8098
51
1. 25
55
39
.8098
.8146
.8195
•8243
.8292
•8342
•8391
50
1.28
53
40
•8391
.8441
.8491
.8541
.8591
.8642
.8693
49
1^31
51
41
.8693
.8744
.8796
.8847
.8899
.8952
.9004
48
1-33
48
42
.9004
•9057
.9110
.9163
.9217
.9271
•9325
47
1^36
79
46
43
•9325
•9380
•9435
.9490
•9545
.9601
•9657
46
i^39
80
43
44
.9657
•9713
.9770
•9827
.9884
•9942
1 .0000
45
1.41
81
1.41
45
1 .0000
1.0058
1.0117
1.0176
I.0235
1.0295
i^0355
44
1^43
1.00
.83
.67
•50
-33
.17
0
Right Hand Column read here
126
GEARING
SPIRAL GEARS
The term spiral gear is usually applied to gears having angular
teeth and which do not have their shafts or axis in parallel lines,
and usually at right angles. Spiral gears take the place of bevel
gears and give a smoother action as well as allowing greater speed
ratios in a given space. When gears with angular or skew teeth
run on parallel shafts they are usually called helical gears.
The Calculation of Forty-Five Degree Spiral Gears
No. of
Thick-
Pitch
Pitch of
Teeth
ness of
Circular
Pitch
(Normal)
of
Pitch
Spiral in
in Spur
Outside
Tooth at
Depth of
Clear-
Cut-
Diam.
Inches to
Same
Diam.
Pitch
Tooth
ance
ter
One Turn
Curva-
Line
ture
(Normal)
Multipl
y by Number of
Add to
Teeth
in Spiral Gear
P.D.
2
0.70710
2.22142
2.828
1. 0000
0.7854
1.0785
0.0785
1.5708
2\
0.62855
1.97464
2.828
0.8888
0.6981
0.9587
0.06^9
1.3963
2\
0.56566
1.77707
2.828
0.8000
0.6283
0.8628
0.0628
1.2566
2f
0.51425
1. 61556
2.828
0.7273
0.5712
0.7844
0.0572
I. 1424
3
0.47140
1.48094
2.828
0.6666
0.5236
0.7190
0.0524
1.0472
zh
0.40406
1.26939
2.828
0.5714
0.4488
0.6163
0.0449
0.8976
4
0.3535s
1.11071
2.828
0.5000
0.3927
0.5393
0.0393
0.7854
s
0.28283
0.88853
2.828
0.4000
0.3142
0.4314
0.0314
0.6283
6
0.23570
0.74047
2.828
o.2,Z3?>
0.2618
0.3595
0.0262
0.5236
7
0.20203
0.63469
2.828
0.2857
0.2244
0.3081
0.0224
0.4488
8
0.17677
0.55S34
2.828
0.2500
0.1963
0.2696
0.0196
0.3927
9
0.15714
0.49367
2.828
0.2222
0.1745
O.2307
0.017s
0.3491
lO
0.14143
0.44431
2.828
0. 2000 ■
0.1571
0.2157
0.0157
0.3142
II
0.12856
0.40388
2.828
0.1818
0.1428
0.1961
0.0143
0.2856
12
0.11785
0.37024
2.828
0.1666
0.1309
0.1798
0.0131
0.2618
14
O.IOIOI
0.31733
2.828
0.1429
0.1122
0.1541
0.0112
0.2244
i6
0.08836
0.27759
2.828
0.1250
0.0982
0.1348
0.0098
0.1963
i8
0.07855
0.24677
2.828
O.IIII
0.0873
0.1198
0.0088
0.1745
20
0.07071
0.22214
2.828
O.IOOO
0.0785
0.1079
0.0079
0.1571
22
0.06428
0.20194
2.828
0.0909
0.0714
0.0980
0.0071
0.1428
24
0.05892
0.18510
2.828
0.0833
0.0654
0.0898
0.0065
0.1309
26
0.05437
0.17081
2.828
0.0769
0.0604
0.0829
0.0060
0.1208
28
0.05050
0.1586s
2.828
0.0714
0.0561
0.0770
0.0056
0.1122
30
0.04713
0.14806
2.828
0.0666
0.0524
0.0719
0.0053
0.1047
32
0.04425
0.13901
2.828
0.0625
0.0491
0.0674
0.0050
0.0982
36
0.03929
0.12343
2.828
0.055s
0.0436
0.0599
0.0043
0.078s
40
0.03533
0.1 1099
2.828
0.0500
0.0393
0.0539
0.0039
0.0873
48
0.02944
0.09249
2.828
0.0417
0.0327
0.0449
0.0033
0.0654
In considering speed ratios for spiral gears the driving gear can
be taken as a worm having as many threads as there are teeth and
the driven as the worm wheel with its number of teeth, so that one
revolution of the driver will turn a point on the pitch circle of the
driven gear as many inches as the lead of the teeth of the driver.
4S-DEGREE SPIRAL GEARS
127
Divide this by the circumference of the pitch circle of the driven gear
to get the revolutions of the driven.
While the subject of spiral gears is rather complex if considered
broadly, most of the difficulties disappear when they have a tooth
angle of 45 degrees. It is perhaps for this reason that from 75 to 90
per cent, of the spiral gears used are made with this angle.
This has the added advantage of being the most durable, although
there is but a trifling increase in wear down to 30 degrees and the wear
at 20 degrees is not serious. In cases of necessity even 12 degrees
can be used without destructive wear.
Where higher speed ratios than can be had with a 45-degree angle
tooth are necessary, they can be laid out as will be shown later and
can be cut on most milling machines. The usual change gears allow
about two thousand different spirals to be cut.
Where the angles are not 45 degrees, the gear with the greatest
angle must always be the driver.
All of the tooth parts are derived from the normal pitch while the
pitch diameters are derived from the circular pitch. These are never
the same in two gears of a pair except when both are 45 degrees.
As the diameter of a spiral gear does not indicate its speed ratio,
the terms driven and follower are used in place of gear and pinion.
45-DEGREE SPIRAL GEAR
These gears are the simplest of all spirals to lay out and to make,
the required speed ratios being obtained by varying the diameters,
precisely as with spur or bevel gears, the rules for the speed ratio
being the same in both cases. Moreover, the various factors required
in laying out and making such gears can be reduced to the simple
table shown.
Such a table has been worked out by E. J. Kearney. With it any
one can quickly make the few calculations connected with any pair of
45-degree gears having teeth between 2 and 48 diametral pitch.
This table will be found on preceding page :
128
GEARING
Example
Let it be desired to construct a pair of spiral gears with 35 teeth in
the gear and 16 teeth in the pinion, using a 10 pitch cutter. Using
table on page 126 we have
Pitch diameter = 0.14143 X 35 = 4-95o.
Outside diameter = 4.950 + 0.200 = 5.150.
Pitch in inches to one turn of spiral = 0.44431 X 35 = 15.550.
Note. — A slight variation in one turn makes no practical dif-
ference, hence the ordinary change gears furnished with a universal
miller will usually be found sufficient.
Number of teeth in spur with same curvature = 2.828 X 35 =
98.980.
Looking at B & S spur-gear cutter hst, we see that 99 is between
55 and 134, therefore we select a No. 2 cutter.
In a similar manner using 16 as a multiplier we obtain the data for
the pinion. This gives 2.262 as pitch diameter so that the center
distance = 4-95o + 2.262 ^ ^^^^^
2
The Various Dimensions Follow
Gear
Pinion
Number of teeth
35
4.950
5-150
15.550
45
10
2
0.216
90
3.6
16
Pitch diameter
2.262
Outside diameter
2.462
7.108
45°
10
3
0.216
Pitch in inches to one turn
Angle of spiral . .
Pitch of cutter
No. of cutter
Whole depth of tooth
Angle of shafts
0
Center distance of shafts
06
FIGURING SPIRAL GEARS
As there is no direct solution for a pair of spiral gears their
calculation is a tedious process and the result must be found
by trial.
As numerous calculations are absolutely necessary, this formula
should not involve division by large or fractional numbers and should
contain the fewest possible operations. Such formulas are:
Let
Then,
SPIRAL GEARS 129
C = Center distance,
P = Diametral pitch,
iVi = Number of teeth in the driver,
iV^2 = Number of teeth in the follower,
Si = Spiral angle of driver,
S2 — Spiral angle of follower.
r — {sf^cdnt Si Ni) + {secant S2 N2)
That is, the sum of the secant of the driving angle times the number of
teeth in the driver, and the secant of the follower angle times the
number of teeth in it divided by the diametral pitch equals twice the
center distance. This formula is derived as follows: The secant of
the spiral angle times the pitch diameter of a spur gear of the same
number of teeth and pitch equals the pitch diameter of a spiral gear
of that angle, the pitch of the spur gear being the same as the normal
pitch of the spiral gear. Now for a spur gear the number of teeth
divided by the diametral pitch equals the pitch diameter. Therefore,
the secant of the spiral angle X — = the pitch diameter of a spiral gear.
The combined pitch diameters times the center distance are equal to
f Secant Si X — ) + f Secant S2 X — '")
or (secant Si Ni) + (secant S2 N2) for one diametral pitch.
The quantity secant Si Ni is the pitch diameter for the driver and
secant S2 N2 is the pitch diameter of the follower. To obtain the
center distance for any other pitch, it is simply necessary to divide
this last result by that pitch.
A table of secants will furnish constants covering the entire range
of angles; and therefore, ail possible solutions for a pair of gears.
After long experience in calculating spiral gears these are recommended
by C. H. Logue as the best and simplest for all cases.
Points to be Kept in Mind when Calculating Spiral Gears
To assist in their use the following points should be kept in
mind:
1. The diameter of a spiral gear increases with its angle.
2. Therefore, the diameter of the follower will reduce as the driving
angle is increased, although not necessarily in the same ratio.
3. It is quite possible for the center distance to remain practically
constant through quite a range of angles, the follower decreasing as
the driver is increased. This is especially true when the gear having
the greater number of teeth is the driver.
I30 GEARING
4. If the center distance is too great when the driving angle is 45
degrees — it must not go below that in any case — a lower number
of teeth must be selected for both driver and follower, while main-
taining the same ratio, and another trial made using a much higher
angle for the driver.
5. The center distance will increase with the angle of the driver.
This increase is more rapid when reducing than when increasing the
speed of the follower.
6. The number of teeth selected for each trial must be in proportion
to the desired ratio.
7. Forty-five degrees is commonly accepted as the most efficient
driving angle.
Selecting Secants and Trial Numbers of Teeth
To calculate a pair of spiral gears, select secants for the desired
angles, assuming the normal pitch, try out the value of 2 C with trial
numbers of teeth for driver and follower.
If the value 2 C is too small increase the number of teeth and try
again. A very few calculations will show the number of teeth to
secure the closest result.
If the center distance thus found is not as desired the angles must
be shifted, keeping in mind the general laws governing the change of
the center distance with the angle.
It is often found that when the desired center distance is reached
the driving angle is too large to be desirable. The only alternative
is to change the normal pitch and try again. A shde rule will give
approximate results.
When there are limitations placed on the diameter of one or both
of the gears the following formula is of value. It may also serve as
a check on the above calculations. The pitch diameters are assumed.
/ pitch diameter of driver X \
\numher of revolutions of driver)
Tan. S\
(pitch diameter of follower X \
number of revolutions of follower.!
This will set a limit on the driving angle Si, to exceed which means
that the gear will be too large.
SPIRAL GEARS 13 1
REAL PITCHES FOR CIRCULAR PITCH
SPIRAL GEARS
The accompan>ang table will be found convenient in figuring
particulars for spiral gearing, as it eliminates much of the work by-
shortening the process, thus making it quite an easy and simple
matter to find the dimensions for either helical gears with axes paral-
lel to each other or for gears with right-angle drive.
Formulas for use with the table are as follows: Circumference on
pitch line = real pitch multiplied by number of teeth.
Lead of Spiral = Circumference on pitch line divided by the tan-
gent.
Pitch Diameter = Circumference divided by 3. 14 16.
For whole diameter add the same amount above pitch line as for
spur wheels of the same pitch as the normal pitch.
The following is an example of the use of the table: A pair of
wheels is required to be: Ratio, 6 to i; normal pitch, i in.; driver,
6 teeth; follower, 36 teeth; angle for driver, 66 degrees; angle for
follower, 24 degrees.
Referring to the table we find that the real pitch for the driver
is 2.4585.
2.4585 X 6 {teeth) = 14.751 {circumference on pitch line).
Cir. 14.751 -^ 2.246 {tangent) = 6.567 {lead of spiral).
Cir. 14.751 ^ 3.1416 = 4.695 {pitch diameter).
For the follower the real pitch is 1.0946.
1.0946 X 36 = 39.4056 {circumference).
Cir. 39.4056 -h 0.4452 {tangent) = 88.512 {lead of spiral).
Cir. 39.4056 -7- 3.1416 = 12.543 {pitch diameter).
Another method of finding the lead of spiral is to multiply the
real pitch by the number of teeth, but for this purpose take the
real pitch of the mating wheel.
In the above example we should have
Real pitch of follower, 1.0946 X 6 = 6.5676 {lead of spiral).
Real pitch of driver, 2.4585 X 36 = 88.506.
It wiU be noticed that there is a slight difference in the result
but this is unimportant, as it is only brought about by the dropping
of a few decimal points in the tangent.
132
GEARING
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.^00 MOOioOiOMr-rfHOOO-tcoc. cscsco tCO O cs o O O oi &i ^ ir>ih i^ O ^
1^ S ?! ?! ??????;C !^'2 ^ Sr^ O O M ci CO t lOO c- O O m co too as O <n Ti-O O H
qqqqoqqqqoqqqqoMHMHHMHHMcscscsMMcscoco <o^ co m-
r- t^oo ^+0 t^ O CO O looo t'tcoiOMwOOOO»rtOOco^cs-+c)Or~0'tM>Dcs
cc O0»ococot-00 H coo O OOO O M M o cs Q M ?-0 COcOMMrhOio!^ ?vO O ^
IC' ^S. 3 "^S S !1 "^ ^ 5i '^'^ ^ "^^ =^ o '^^ o '^^o "5=0 too <^ w xo M OO ?5 H
t-MOO ti-;oc:o tM q O t-O uptcOMMi-jOO ooo OO r- t^ t^O O i/5iotott-*t
>AlA44-^COCOCOCOCOCSMciMMC^CSMCSC<C<HMHl-iMHl-il-;MWHMHMM
S^
t to 0 OOoCMOCtMcrO too •i-'^ O 0 tcsoocO m tMOO tO <s t tJ- t t t
52 -^ 3^ MiooioOiOMr^coOr-iococi m o 0 O m co »ocO m i/^ O .o m o r-O O r^
§8c^cg^^ag^oo^ss§;SoSS;'&8;8 3 o o^Jo'^^s 8^:^ 2 2-:i?^?^ ;?
d d d d d d d d d d d d d d d d d d d M H H hJ M H H M H hi i-i w H H H H H
1
?i?>8So^^§i'=2;;5?;:5s::-&gs.^cg;c^^^^c;=^^?^^-ocoxoco
•OttCOCOCOCOCSMM'cse^'cSCSC^aMIHMHHHMHMI-ll-iMt-iMMHiMHWM
O H M cotv-<0 t~-00 OO M M co%°ioO°t^oO°0°0°M°ci°co**t°iooVoo'o°0*w*«°co'*'t°t/l
Ml-,Ml-llHMMM^Hl-l<^^csc^c^MP^c^<^^c^c^cocococococococococotttttt
O OcO i^O ui t CO M M O ooo t^O vo t CO cs m O OoO t~-0 lo t co M m °0 °Ooo °f^u5 "lo
=0 t^r^r-t^r-t^t^t^r^ t^O OOOOOOOOO «r,ioioioio>oi/^ioioio 4 t t^ t
134
GEARING
SPUR-GEAR CUTTERS FOR SPIRAL GEARS
Number of Teeth in the Spiral Gear
gsi§g s § § g; § 5S ^ s g KSEKtrs.
s o
|l!llli!i||t:l!lV l!;iMlini\':|i|!lNI ll \.r
1 N KN
^
_
^
-n-iii" ;"""^
\J^aX N
'4
Mm s, "^
t \3.^
^ ^^ ^
:;:::::: r:
s
«> S ^
s
Z%- \- X
s.
:::::::.__ _. i:
t ^_
^J^ \ ^
s
5' 's
\
s
.
??
^ ~ ^^
\
\
. \L
m
-^- ^
s.
s
., S
t£
V v
\
1
..It—
-_\ 5
i
ra ti
^^
\
\
o
!Mi|!MIIIIIIIIIIIII
\
^
.., ■ ■ , L
H'l
■^
\
•: ' ^i—rf
W V
~~' S
\
: iV, ! iiii 1 V.
'~~' \
\,
g
o
il i 1 "^-11 s
\
\
^! %] ---,----
^
111 <;
111 1 V
\
jl ::::::::;::::::^;
\^
\
\
^1 I
s
\^
0
II
\
i
"'" \
l!
\
o
\
o
\
\
\
i 1 . 1
s
To find the number of a spur-gear cutter to be used in cutting a given
spiral gear, locate the intersection of lines traced from the points
representing the number of teeth and the spiral angle on the two
scales. The number in the area on the chart within which the inter-
section falls is the cutter number of Brown & Sharpe's involute cutter
system required.
SPIRAL GEAR TABLE 135
SPIRAL GEAR TABLE
While it is better in every case to understand the principles in-
volved before using a table as this tends to prevent errors, they can
be used with good results by simply following directions carefully.
The subject of spiral gears is so much more complicated than other
gears that many will prefer to depend entirely on the tables.
This table gives the circular pitch and addendum or the diametral
pitch and lead of spirals for one diametral pitch and with teeth hav-
ing angles of from i to 89 degrees to 45 and 45 degrees. For other
pitches divide the addendum given and the spiral number by the
required pitch and multiply the results by the required number of
teeth. This will give the pitch diameter and lead of spiral for each
wheel. For the outside diameter add two diametral pitches as in
spur gearing.
Suppose we want a pair of spiral gears with 10 and 80 degree angles,
8 diametral pitch cutter, with 16 teeth in the small gear, having 10-
degree angle and 10 teeth in the large gear with its 80-degree angle.
Find the lo-degree angle of spiral and in the third column find
1.0154, Divide by pitch, 8, and get .1269. Multiply this by num-
ber of teeth — .1269 X 16 = 2.030 = pitch diameter. Add 2
pitches — two i = J and 2.030 + .25 = 2.28 inches outside diameter.
The lead of spiral for 10 degrees for small wheel is 18.092. Divide
by pitch = 18.092 -^ 8 = 2.2615. Multiply by num^ber of teeth,
2.2615 X 16 = 36.18, the lead of spiral, which means that it makes
one turn in 36.18 inches.
For the other gear with its 80-degree angle, find the addendum,
5.7587. Divide by pitch, 8, = .7198. Multiply by number of
teeth, 10 = 7.198. Add two pitches, or .25, gives 7.448 as outside
diameter.
The lead of spiral is 3. 1 90 1. Dividing by pitch, 8 = .3988. Multi-
plying by number of teeth = 3.988 the lead of spiral.
When racks are to mesh with spiral gears, divide the number in
the circular pitch columns for the given angle by the required dia-
metral pitch to get the corresponding circular pitch.
If we want to make a rack to mesh with a 40-degree spiral gear
of 8 pitch: Look for circular pitch opposite 40 and find 4. loi. Divid-
ing by 8 gives .512 as the circular pitch for this angle. The greater
the angle the greater the circular or linear pitch, as can be seen
by trying an 80-degree angle. Here the circular pitch is 2.261
inches.
136 SPIRAL GEAR TABLE
SHAFT A1-3GLES 90° FOR ONE DIAMETRAL PITCH
^1
•Eg
diameter,
diametral
: quotient
■r.of teeth
diameter,
diametral
quotient
r of teeth
^1
s
u,-a
^ifl
To obtain the lead of
u^
w
3 ^
spiral, divide by the
-1^
3-^
&
^"S
•H-'i-'E i
required
diametral
Q
Q
o^ja
m
pitch and multiply
?2tJ
■S'2-a
a
H
u > "
quotient by the re-
l|il
ii.^H
•S
•R
■S'S'S,
quired
number of
1-3-S,
1
w
•s
cfg
5 0 '^ a
teeth
■ml
•111
'cl
III
0 o-v
nn
0^ 5^
0 o-o
5P
h
h
H
h
<
Circular
Pitch
One
Tooth or
Addend
Lead of Spirals
One Tooth
or
Addendum
Circular
Pitch
Small
Small
SmaU
Small
Large
Large
Large
Large
Wheel
Wheel
Wheel
Wheel
Wheel
Wheel
Wheel
Wheel
I
3-1419
l.OOOI
180.05
3-1420
57-298
180.01
89
2
3.1435
1 .0006
90.020
3-1435
28.653
90.016
88
3
3-1457
I.00I3
60.032
3-1458
19.107
60.026
87
4
3-1491
1.0024
45-038
3-1492
14-335
45.035
86
5
3-I53S
1.0038
37-077
3-1527
11-473
36.044
8S
6
3-1 5S9
1-0055
30.056
3-1589
9-5667
30.055
84
7
3-1652
1.0075
25-728
3-1651
8.205s
25-778
83
8
3-1724
1.0098
22.573
3-1724
7.1852
22.573
82
9
3.1806
I.OI24
20.0S2
3-1807
6.3924
20.082
81
10
3.1900
1. 01 54
18.092
3-1901
5-7587
. 18.092
80
11
3.2003
1.0187
16.464
3-2003
5-2408
16.464
79
12
3-2145
1.0232
15.076
3-210S
4-8097
15.104
78
13
3.2242
1.0263
13-966
3.2294
4-4454
13-988
77 •
14
3-2377
1 .0306
12.986
3-2378
4-1335
12.986
76
IS
3-2522
1-0352
12.138
3-2524
3-8637
12.138
75
16
3.2679
1 .0402
11-393
3-2678
3-6279
11-397
74
17
3.2848
1.0456
10.417
3.2821
3-4203
10.745
73
18
3-3116
1.0514
10.192
3-3032
3.2360
10.166
72
19
3-3225
1.0576
9-6494
3-3225
3-0715
9.6494
71
20
3-3430
1. 0641
9.1848
3-3433
2.9238
9.1854
70
21
3-3650
1.0711
8.7662
3-3652
2.7904
8.7663
69
22
3-3882
1.0785
8.3862
3-3833
2.6694
8.3862
68
23
3-4127
1.0863
8.0309
3-4129
2-5593
8.0403
67.
24
3-4061
1.0946
7-7379
3-4391
2.4585
7.7242
66
^1
1-1033
7-4332
3-4663
2.3662
7.4336
65
26
3-4953
1.1126
7.1664
3-4952
2.2811
7.1663
64
27
3-5258
1. 1223
6.9198
3-5257
2.2026
6.9197
63
28
3-5579
1-1325
6.6912
3-5575
2.1300
6.6916
62
29
3-5918
1-1433
6.4799
3-5919
2.0626
6.4799
61
30
3-6276
I -1 547
6.2778
3.6277
2.0000
6.2832
60
31
3-6650
I. 1666
6.0979
3-6652
1.9416
6.0997
59
32
3-7043
I. 1791
5-9282
3-7044
1.8870
5.9282
58
33
3-7457
1.1923
5.7710
3-7459
1.8360
5-7680
57
34
3-7894
1.2062
5.6181
3-7826
1.7882
5.6178
56
35
3-8349
1.2207
5-4754
3-8351
1.7434
5-4770
55
36
3-8830
1.2360
5-3431
3-8834
1.7013
5-3448
54
37
3-9336
1.2521
5.2201
3-9261
1.6616
5.2200
53
38
3-9867
1.2690
5.1028
3-9921
1.6242
5.1026
52
39
4.0482
1.2867
4.9866
4.0416
1.5890
4.9920
51
40
4.1010
1-3054
4.8873
4.1012
1-5557
4.8874
50
41
4.1626
1.3250
4-7885
4-1540
1.5242
4.7884
4?
42
4-2273
1-3456
4-6949
4.2272
1.4944
4.6948
48
43
4-2956
1.3673
4.606s
4.2956
1.4662
4.6062
^1
44
4-3671
1.3901
4-5223
4-3675
1-4395
4-5225
46
45
4-4428
1. 4142
4.4428
4.4428
1.4142
4.4428
45
THREADS OF WORMS 137
THREADS OF WORMS
Worms are cut with threads having a total angle of 29 degrees,
similar to the Acme thread. Some use the same proportions as for
the Acme, but most use a deeper thread such as the Brown & Sharpe,
which is .6866 deep instead of .51 for a one-inch pitch as in the Acme.
It is not easy to cut odd fractional pitches in most lathes-, so regular
pitches are cut and the circular pitch of the worm wheel is allowed
to come in fractional measurements for pitch diameters and center
distances. Having determined on the reduction as 40 to i, the rel-
ative proportions can be considered as follows:
Assume a thread of 4 to the inch for the worm or a lead of I inch.
Then as the reduction of 40 to i there must be 40 teeth in the worm
gear, I inch from center to center of teeth or 10 inches in circum-
ference on the pitch line or 3.18 inches. If a reduction of 20 to i
is wanted we can use the same gear but cut a double thread of 2 per
inch, which will give the same distance between teeth, but the worm
gear will be moved two teeth every revolution of the worm.
Some of the commonly used proportions are:
_,.,,. r No. of teeth X pitch in inches
Pitch diam. of worm gear = ^ .
3.1416
T^- 1-1 ^.1416
Diametral pitch = — r^ : — 7.
Linear pitch
Throat diam. of worm gear = Pitch diam, 4- ttt tt^tt.'
^ Diam. Pitch
Outside diameter of gear for 60° sides = throat diameter + 2 (.13397
throat radius.)
Whole depth of tooth of worm or worm gear «= .6866 X lineal
pitch.
Width at top of tooth of worm = .335 X linear pitch.
Width of bottom of tooth of worm = .31 X linear pitch.
Outside diam. of worm — single thread = 4 X linear pitch.
Outside diam. of worm — double thread = 5 X linear pitch.
Outside diam. of worm — triple thread == 6 X linear pitch.
Face of worm gear = ^ to f outside diameter of worm.
Width of Face
A COMMON practice for determining the width of face or thickness
of worm wheels is shown in Fig. 15. Draw the diameter of the
worm and lay off 60 degrees as shown; this gives the width of work-
ing face, the sides being made straight from the bottom of the teeth.
Others make the face equal to f the outside diameter of worm, but
^ the diameter of the worm is more common.
138
GEARING
THREADS OF WORMS
139
Table of Proportions of Worm Threads to Run in Worm
Wheels
B.
Width of
Thread
at Top
CQ
00 M lOl-^O N fOU^O r-r^oo -^Ooo OOP) inO>0.0>vO
t^OO 0 " fOi'lN'O fO" 000 t^O iO-*5-fOrOP) M 0 "
vq -> lo -3- CO CJ CJ « M M q q q q q q q q q q q q q
W.
Width of
Thread
Tool
at End
II U
0 »o 0 »n 0 >^^ 0 0 foo >o a 0 t^ <ooo ■* 0 00 w ■* <N
N TTvOOO " COO i^<N 000 r^OO VOtcococON C) M p-
«q lo ^ CO CO cs (N M M « q q q q q q q q q q q q q
^:s^ ;j II
OOOOOOcoOO^OC^OMOcot•J^loo^OI^Ml^.
OJOO'OOJOcoOOOn^MOco^nLoo^^iOMVr.
^coiCsq SiJ^^oJ^S^, MM M 2^^ q^ q q q q q q
W.D.
Whole
Depth of
Tooth
^0
PI 0 Ov co^O 0 r^ co^O 00 NOVO fO-<tM00 coi^ei 0 Ot^
CO M Ovoo ^o 10 r- CO ^00 0 " 0 t^ -^00 lovo 00 r- Ov M r-
l^ 0 <N 1000 M lorft^oi Or^iocOM OvOO t^O >o "^ ■^ co
coc^qoO'Oio^coiNc^MMMMMqqqqqqqq
S.
Depth
of Space
below
Pitch Line
u
+
\O>O»O'<tcON»ONCOl^MH00r~ 'I-VO O OOO t- CO O w
0 ^P) O00<3 lOTt-r^CN IOCS m com mO OO 0>0 coo
CO rr too vO t^ rroo ^ cm 0 OvOO r-vO lOTf-^cococN (N N
r-vq '^t'?"^". ':i". ". ^OQQQoqqqqqq
C.
Clearance
Hi2
0>00>00»OCOOOOCO>OwOCOw<v)lr-, 0<nOmio
0 00 r-O Lococo cm' (NmmmmmOGDo' 00000
Mqqqqqqqqqqqqqqqqqqqqqq
D.
Working
Depth
of Tooth
X
II
Q
p) M aoo vo V-, n- co>o cs om v>cow o^ot^i^o -^oo P)
CO -^ Tt 100 r~ TToo M- P) M ov M r-o M 00 CO CO i^, o> I'-.
r^M loocot^p) M liiMoo i'^ -^ ct 0 Of-r^O lo^^roco
(N M q> t^^q f f ^ fj <^. ". ". « « ►: q q q q q q q q
H.
Tooth
above
Pitch-
Line
Oh*
II
vo o>oo>coi^N p) cow oo 1^ r- M 1000 -^oo »o r- Ov\o
VO t^ 1^ t^OO 00 M Ov t^vO 0 0.0 COCOlOOitOMMS P) 0>J^
coiot-o>MCOMU^P)oar- riv3 lo^cococop) pg m m
vqio'j-cocopjcHMMMqqqqqqqqqqqqq
■
D. P.
Dia-
metrical
Pitch
II
a.'
Q
00 P> ^ covO COtP)OoOO'*P)0>OwI^coO>PiTr tooo
0 lOTfcOMOO P) CO-*-* "-<-0 r-00 0. M P) Tt to 0 P) u-,00
t^ Ov 0 M -^i-oo M 00 10 P) 00 CO 0 •* CN CO r- M 000 0 ^
ioi--q lOM M ^^c^oq "^ o^ ";> ", ^co q> « pj ^^ 9 <^ 'C-
M M ci M CO ■* -*vd r^ Ov 6 PJ 4 >oo6 M >A,od M r^ CO 6 0
„MMMMP<P<P)COCO-<riOlA,
pi.
Threads
•a
r^.I*>«t!-5'«0 HC-!-«M .-«?» .-tN rJCJ
MMMNPtCOPO'^-* 10*0 t>.00 Oi 0 M '*\0 00
C.P.
Circular
Pitch
C „ M M M
o9
^ ^
. ^ 0
•y-^
"2 "^-5
^ ^
^-s
-o <u
>> -2
It
deb
24.
plus
^ «-i (U 3 'T1
rt o
1) CJ
^ E -^ a; ^ ^•
Sill I I
I40
GEARING
SPEEDS AND FEEDS FOR GEAR CUTTING
(Cincinnati Gear Cutting Machine Co.)
Range of dififerent sizes of machines as follows :
No. 3. Up to and including 4 diametral pitch.
No. 4. Up to and including 3 diametral pitch.
No. 5. Up to and including 2 diametral pitch.
No. 6. Up to and including if diametral pitch.
No. 7. Up to and including i diametral pitch.
For Carbon Steel Cutters RxJN>riNG at a Peripher.\l Speed of 35 Feet
PER Minute on Cast Iron and 30 Feet per Minute on Steel
^
1
Feed in In. per Min.
a
Feed in In. per Min.
for Roughing Cut
Feed in In. per Min.
(^ u
Finishing in one
Cut
.010 to .030 in. Left for
for Finishing Cut
■gS
Finishing Cut
Cast
Soft
High
Car-
Nick-
el
Steel
Cast
Soft
High
Car-
Nick-
el
Steel
Cast
Soft
High
Car-
Nick-
el
Steel
Iron
Steel
bon
Steel
Iron
Steel
bon
Steel
Iron
Steel
bon
Steel
I
I 8
I -
I
I
2lV
I 1
If
li
I*
I f
I -
I
I
2t^,
I 8
If
I 4
li
2t^
I -
li
I
2fA
2lV
21^.
I
if
2A
in
It".
3^
2ik
2t^«
lU.
4-^
3s
2H
2t'.
2
2 2
2
lik
li
4tV
3i
2h
2
4t^«
3 i
2 1
2
2^
2 ^
2
iH
4A
3i
2^
2
4i^
3i
2 i
2
3
,^T^ff
2 -
a
4i^-
3t'r
2
2
45
3t'.
2 5
2
4
3t'«-
2 ^
2
if
'^f
3i;6-
2
2
4 ^
318
2 i
2
5
.St'b
2 ^
2
^t
3i'rt
2 -
2
44
3ts
2 ^
2
6
3A-
2 ^
2
I
4i
3/s
2 -
2
4 4
3l'5
2 *■
2
7
.StV
2 ^
2
4i
3A
2 ^
2
4i
3Trt
2 -
2
8
3t'«
2 -
2
i|
.St's
4 s
3/5
2*
.St'b
4-
3/e
2 -
9
4i
3t'.
2 1
2
5t'«
4z
3T'fl
2i
.St'.
4-
3/5
2 -
10
4 i
3t's
2 2
2
Si'e
4i
31^.
2^
Si'.
4 -
3Tff
2 ^
For High Speed Steel Cuttebs Running at a Peripheral Speed of 55 Feet
PER Minute on Cast Iron and 80 Feet per Minute on Steel
rt
■
Feed in In. per Min.
W
Feed in In. per Min.
for Roughing Cut
Feed in In. per Min.
(^ !d
Finishing in one Cut
.010 to .030 in. Left for
for Finishing Cut
IS
Finishing Cut
Cast
Soft
High
Car-
Nick-
el
Steel
Cast
Soft
High
Car-
Nick-
Cast
Soft
High
Car-
Nick-
el
Steel
Q
Iron
Steel
bon
Steel
Iron
Steel
bon
Steel
Steel
Iron
Steel
bon
Steel
I
2
If
If
I ?
I 8
2^
2H
2}.^
2 IB
Is
2 -
2
2
3tHt
3tH.
3t^t
2H
i^
3 ^
2t^
2,^
2l^
4f
4f
4^
3 f
I*
2H
2t\
2t^«
iH
4-
3f
3l
2ii
Sr'k
Sf-.
.SfH
4f
2
3i
2 2
2 8
2 -
I ^
5 -
4
4
3i
6t^.
OtIt
6t1t
5i
24
si
2 -
i^
s -
4
4
3i
6^
6^
6t^.
S i
3
3tV
2 ^
2
2 -
2 -
2
?§
4
4i
3t'.
6H
6t^
<>-^
.SA
4
3i^
2 §
2 J
2
4
44
44
3t^.
OH
6 ^
6 :?-
6^S
5
3tV
2
St^
4 -
3t'.
6tS
6i
6 i:
6 i
bj
6
4t
3i^s
3f.
^1
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87
MILLING AND MILLING CUTTERS
MILLING MACHINE FEEDS AND SPEEDS
The determining of the proper feeds of milling cutters in the past
was usually a matter of guesswork, or experience, as a good many
would term it, no absolute rule of any kind having ever been
established.
A guide for determining the proper feed of milling cutters is found
in ascertaining the thickness of the chip per tooth of the cutter.
Taking, for example, an average size milling cutter working in
cast iron, say 2§ inches diameter, 3 inches long, with eighteen teeth,
which is quite commonly used, and it will be found that the thick-
ness of the chip per tooth is quite small, resulting in .0018 inch, with
a table feed of 2 inches per minute. This is entirely too slow. Now,
comparing this cut of .0018 inch with a lathe tool cut, it will be seen
that such a chip in a milling cutter is much smaller and is far more
injurious to the cutter than a heavier feed, since the cutting edge of
a tool will hold up longer in cutting into the metal instead of scrap-
ing it.
A cutter is very seldom ruined by the feed, but is generally ruined
by overspeeding it. For instance, with a cutter of thirty teeth with a
table feed of .300 inch per revolution, the chip per tooth will then
.300
only be — j^ = .010 inch thick — still quite a light cut when compar-
ing it with a lathe tool chip. Hence in many cases of milling, if the
feeds are guided by the thickness of chip per tooth, a much faster
feed would be used, since it is evident that the heaviest feeds, com-
aratively, give only a thin chip per tooth.
Cutting Speeds
The Brown & Sharpe Mfg. Co. recommends a cutting speed of 65
feet per minute for carbon and 80 to 100 feet per minute for high
speed milling cutters under average conditions. On soft cast iron,
having a tensile strength of about 13,000 pounds — the feed recom-
mended is 0.148 inches per revolution or about 9 inches per
minute for carbon cutters. With a medium cast iron of about
23,000 pounds tensile strength, the same speed is maintained but
the feed reduced about f or to 6 inches per minute. For high speed
cutters the feed can run up to 0.26 inch per revolution on the softer
iron.
141
142 MILLING AND MILLING CUTTERS
On steel of 65,000 tensile strength, with a cut 6 inches wide by y\
inch deep, a feed of 16 inches per minute can be maintained for long
periods. At 60 revolutions per minute and a feed of 0.262 per revo-
lution 18 cubic inches per minute was removed with 21 horse-
power.
It is not always advisable to maintain the highest cutter speeds as
a slower speed and heavier feed will prevent vibration and chatter.
These are not maximum results but. can be attained under regular
working conditions. The horsepower required for removing a cubic
inch of metal per minute on the milling machine may be safely con-
sidered as if horsepower for steel and f horsepower for cast iron.
The Action of a Milling Cutter
Experiments carried on with cutters at the works of the Cincinnati
Milling Machine Company and extending over several years, have
led to results of general interest. These tests covered milling cutters
of various types.
The action of the ordinary milling cutter is not a true cutting
action, as it is commonly understood. By a true cutting action is
meant the driving of a wedge-shaped tool between the work and the
chip and, although this definition is not based on a generally accepted
meaning of the term, it is believed that it expresses fairly well what
most mechanics understand by cutting. Practically all milling
cutters have their teeth radial and this, of course, excludes the possi-
bility of driving a wedge between chip and work. The tooth com-
presses the metal until it produces a strain great enough to cause a
plane of cleavage at some angle with the direction of the cutter. It
then begins to compress a new piece, push it off, and so on. This at
least seems to be the action of the cutter, judging by the form of the
chips. These chips are in the form of needles or small bars.
The chip taken by a milling cutter varies very materially from
those taken by a lathe or planer tool. These latter tools make chips
of uniform section, whereas the section of a milling chip increases
from zero to a maximum.
Fig. I shows a milling chip as it would appear, if no compression or
distortion took place. The proportions are very much exaggerated, so
as to bring its typical shape clearer into view. The width A B at
the top is equal to the feed per tooth. The height B Cis the depth of
cut. The length B D is the width of cut. The section M N 0 P,
shown halfway on the chip, is a normal section and a measure of the
amount of work which was done at the time the cutter passed the
point M.
Fig. 2 shows the action of a milling cutter, with center 0, when the
cutter is rotating and the work is feeding at the same time. The
tooth A B sweeps through the path B C. When the point B has
reached the position Bi, a new tooth starts cutting. By this time O
has advanced to position O2, and the new tooth A2 B2 is not yet in a
vertical position, when the point B2 touches the work. When the
ACTION OF CUTTER TOOTH
143
cutter revolves, this point B2 must penetrate into the work and com-
press the metal of the work. The result will be spring in the arbor.
When this spring has assumed certain proportions, the blade or tooth
Fig. I — Chip As- Fig. 2. — Action
sumed to be pro- of Milling
duced by Cutter Cutter
without distortion
Fig. 3. — Coarse pitch
Milling Cutter
begins to remove a chip. This may be assumed to take place in the
position Bz, the tooth simply gliding over the work from B2 to Bz.
This action must necessarily be very harmful to the cutter, and it
was believed that this, perhaps more than any other action of the
cutter, caused its dulling. It would be especially severe with hght
cuts, as a relatively small amount of spring would allow the point
B2 to travel through a large arc. It would be quite possible that a
tooth should fail entirely to take a chip, and that the succeeding tooth
would take a chip of double the amount.
This peculiar action of the milling cutter is inherent in its con-
struction and cannot be avoided. This question then is how to
minimize these harmful results.
Another feature, which limits the ability of a milling cutter to
remove metal, is the proportion between the chip to be removed and
the amount of space between two adjoining teeth. Such a limitation
does not exist with lathe or planer tools, where the chips have un-
limited space in which to flow off.
Form of Tooth in the New Cutter
The foregoing considerations led to a gradual evolution of spiral
milling cutters. At first, the number of teeth of spiral mills was only
slightly diminished, as it was thought that some element which was
not considered might aflfect the result. Gradually the spacing was
increased and the cutters, as now used, have taken the forms shown
in Fig. 3.
Two standard sizes are used, although other sizes are required for
special cutters and special gangs. The standard diameters are 3I
inches and 4^ inches. The 3|-inch diameter cutters are made with
nine, and the 4^-inch diameter cutters with ten teeth, which corre-
sponds to a spacing of about i\ inches. The point of the tooth has a
land of 3V inch, and the back of the tooth forms an angle of 45 degrees
with the radial line. The chip space is approximately four times as
great as in the usual standard cutter of the present time and is formed
with a y\-inch radius at the bottom.
144
MILLING AND MILLING CUTTERS
Results of Tests
Very satisfactory results were obtained with these cutters. Figs.
4, 5, and 6 show the results of tests made with cutters mth |-inch,
■f-inch and i|-inch spacing. Cuts were taken on cast-iron test
14
IS
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2 4 6 8 10 12 14 16
Feed, Inches per Minute
2 4 6 8 10 18 14 16 13
Feed, Inches per Miaute
2 4 e 8 10 12 14 le 18
Feed, Inches per Minute
Milling Cutters and their Efficiency
blocks. It will be noticed that the same amount of power is required
to take a cut j-inch deep and with 10.4 feed with a cutter of |-inch
pitch, and a cut \ inch deep and with 13.5 feed but with a cutter
1 1-inch pitch.
Therefore there is a large increase in the amount of metal which
can be removed with the same amount of horsepower, by using these
wide-spaced cutters. It was also found that for roughing on the ordi-
nary work in the shop a cutter with the wider-spaced teeth would
remain sharp for a longer period, notwithstanding that feeds had been
increased.
The Finish of the Work
It is a common belief that better finish can be obtained with teeth
closely spaced, but experience with the wide-spaced cutter shows that
there is no ground for this belief. The grade of finish may be ex-
pressed by the distance between successive marks on the work. These
marks are revolution marks and not tooth marks. It is practically
impossible to avoid these revolution marks. They are caused by
the cutter not being exactly round or quite concentric with the hole,
by the hole not bemg of exactly the same size as the arbor, by the
arbor not being round, by the straight part of the arbor not being
concentric with the taper shank, by the taper shank not being round
or of the same taper exactly as the taper hole in the spindle, by this
taper hole being out of line with the spindle, by looseness between
the spindle and its bearings, etc. Each of these items is very smaH
in any good milling machine; yet the accumulation of these Httle
errors is sufficient to cause a mark, and this mark needs to have a
depth of only a fraction of a thousandth of an inch to be very plainly
visible. As these marks are caused by conditions which return once
for every revolution of the cutter, it is plain that the spacing of the
teeth can have no effect on the distance between them and, therefore,
Qn the grade of finish. This has been proven by actual tests.
TAPER SHANK END MILLS
145
The Chip Breaker
It is generally believed that for finishing alone a milling cutter
should be used without chip breakers, the effect of the chip breaker
being to scratch the surface. To overcome this trouble, chip break-
ID R.H. Spiral 8 Teeth ^./[^ j
Fig. 8. — Taper Shank End Mills
ers are made as shown in Fig. 7 with clearance at both corners. This
prevents the tearing up of metal with the result that a cutter with
these chip breakers produces as good a finish as one without chip
breakers.
End Mills
Fig. 8 shows the end mills which are now considered standard by
the Cincinnati Milling Machine Company and which fill practically
all requirements. They are made in sizes of i inch, i^ inches, i^
146
MILLING AND MILLING CUTTERS
inches and 2 inches in diameter, the smallest with four, and the
largest with eight teeth. In order to preserve the strength of the
teeth it is necessary to mill the back of the teeth of the three smaller
sizes v/ith two faces. Their action is remarkably free. A 2-inch
taper shank end mill milled a slot ixV inches deep in a solid block
of cast iron at a rate of 6 inches per minute. The block was
Spiral Shell Cutters
clamped to the table of the milling machine and the knee was fed
upward. The same cutter would remove from the end of the casting
a section i| inches wide and i| inches deep. Under the latter con-
ditions, the chips would free themselves from the cutter and these
chips were rolled up in pieces much like the chips obtained from a
broad planer tool, when taking a finishing cut. This cut was taken
with a feed of 1 1 inches per minute. Another similar cut, but i inch
and 1 1 inches in section, was taken with a feed of ^s inches per
minute.
SHELL END MILLS
147
Fig. 9 shows the shell end mills of the wide-spaced type, which
are now considered standard for their use by the Cincinnati Milling
Machine Company, and Figs. 10 and 11 show the side mills.
'/32'' 6' Diam.
- Side Mills
When milling steel, a heavy flow of oil on a milHng cutter, forced
by means of an oil pump, is just as essential as the great volume of
oil which is used on automatic screw machine tools, which would
not hold up one-half hour if not so flushed. The life of a milling
cutter amply lubricated will be materially prolonged and it will be
capable of standing a much heavier feed.
Tan a
Leads or B. & S. Cutter Spirals
The leads of the Brown & Sharpe Cutter
Spirals are as follows:
Tan a =
Diam. of Cutter
Lead
Diam. of Cutter
Lead
h"
7.29" .
2"
31.5"
f- f"
9-52"
2i-2|"
36"
i"
13-71"
2f-3"
48"
I -li"
17.14"
2>h-2>\"
60"
n"
23-33"
a"
68.57"
If"
28"
148
MILLING AND MILLING CUTTERS
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TABLE OF PITCHES AND ANGLES 149
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ISO
MILLING AND MILLING CUTTERS
U
To find the angle for cutters of a larger diam-
eter than given in the table, make a drawing as
shown in the diagram; the angle b being a right
angle. Let b c equal the circumference. Let a b
equal the pitch. Connect c a by a line, and
measure the angle a with a protractor; or divide
^ the circumference by the lead and the quotient will
be the tangent of the angle. Find the angle in a
table of tangents.
Diameter of Mill, Cutter, or Drill to be Cut
Inches
Values Given Under Diameters are Angles in Degrees
T^
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TABLE OF PITCHES AND ANGLES 151
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152
MILLING AND MILLING CUTTERS
MILLING HEART-SHAPED CAMS
One method of producing heart-shaped cams is as follows:
Lay out the curve of the cam roughly, as in Fig. i. Drill and re-
move the outside stock, being sure to leave sufficient stock to over-
come errors in laying out. Put the cam on the nut arbor and tighten
securely. If the roll of the cam is | radius, select a milling cutter
having the same radius, as the roll of the cam must come to the lowest :
point, which it would not be able to do if a cutter of a smaller radius
than that of the roll were used. It would also make a difference to
the other points on the curve of the cam, which is not quite so
apparent at first glance.
Fig. I. — Method of Laying
Out Cam
Fig. 2. — Position of Cam and
Cutler when Commencing
to Mill
Selecting an Index
The next operation is to place the cam between centers on the
milling machine, having the cutter in line with the vertical radius
of the cam, at its lowest point. Next choose an index circle which
will give a division of the cam such that the rise of each division will
be in thousandths of an inch, if possible. For this cam take a circle
which will give 200 divisions. As this will make 100 divisions on
a side, the rise of each division will be o.oii of an inch. Now raise
the table to the required hight, starting at the lowest point of the
cam, and mill across, as in Fig. 2.
MILLING CAMS 153
Moving the Table
For the other cuts lower the table o.oii each time, and revolve
the cam one division until the highest point of the cam is reached,
then raise the table o.oii for each division of the cam.
When the cam comes from the milling machine there will be found
to be small grooves left between the cuts. These may be easily
removed by smoothing off with a file without impairing the accuracy
of the cam.
Most screw-machine cams can be made in this manner, and thev
will be found to be more accurate than if laid out and filed to the
line, and also much easier to make after one has become accustomed
to the method.
MILLING CAMS BY GEARING UP THE
DIVIDING HEAD
By the method here shown, cams of any rise may be milled with
the gears regularly furnished with the milling-machine.
\
b
Angle of E/levation \ ^
of Index Head
.V.
-Lead for vrbicb Milling Machine is Geared-
FlG. 3,— Diagram for Angle of Index Head
With the head set vertically the lead of the cam would be the same
as the lead for which the machine is geared, while with the head
horizontal and the milling spindle also, a concentric arc, or rest, would
be milled on the cam, regardless of how the machine was geared.
By inclining the head and milling spindle, we can produce any lead
on the cam less than that for which the machine is geared.
The method of finding the inclination at which to set the index
head is shown in Fig. 3, and is simply the solution of a plain right-
angled triangle, in which the hypothenuse represents the lead of the
machine, and one of the other sides represents the lead we wish to
produce on the cam. By dividing the latter by the former we get
the sine of the angle of inclination.
Take for illustration a plate cam having |-inch rise in 300 degrees.
^60
which is the lead we want on the cam, while the slowest lead for which
the B & S. machine can be geared is 0.67
0.15
—— = 0.234.
IS4
MILLING AND MILLING CUTTERS
Consulting a table of sines, we find 0.224 approximates closely the
sine of 13 degrees, which is the angle at which to set the head, and
if the milling spindle is also set at the same angle, the edge of the
cam will be parallel with the shaft on which it is to run. Fig. 4
shows a milling-machine set for this job.
When a cam has several lobes of different leads, we gear the
machine up for a lead somewhat longer than the longest one called
for in that cam, and then all the different lobes can be milled with
the one setting of gears, by simply altering the inclination of head
and milling spindle for each different lead on the cam.
If the diameter of the cam and the inclination of the head will
admit, it is better to mill on the under side of the cam, as that brings
the mill and the table nearer together and thus increases rigidity,
besides enabling us to easily see any lines that may be laid out on
the flat face of the cam. Also the chips do not accumulate on the
work.
Fig. 4- — Dividing Head Set for Cam Milling
The work is fed against the cutter by turning the index crank,
and on coming back for another cut we turn the handle of the milling-
machine table. As a result the work will recede from the cutter
before the cam blank commences to turn, owing to back lash in the
gears, thus preventing the cutter from dragging over the work while
running back.
In this way we use to advantage what is ordinarily considered a
defect in machine construction.
The milling -machine, when used as shown in Fig. 4, will be found
to be more rigid than when the head is set in the vertical position,
and the cams will work more smoothly on account of the shearing
action of the cutter.
One possible objection to the method here advocated is the neces-
sity of using, in some cases, an end mill of extra length of tooth. In
practise, an end mill |-inch diameter and with a 3J-inch length of
tooth is not unusual; but the results in both speed and quality will
be found entirely satisfactory.
MILLING SCREW MACHINE CAMS 155
TABLES OF SETTINGS FOR MILLING SCREW
MACHINE CAMS
Computed by the Cincinnati Milling Machine Co.
On the preceding pages an explanation is given of the methods of
computing the angle at which to set the dividing head and milling
head for cutting spiral screw machine cams or other cams of similar
form to any desired lead. For leads below 0.6 inch the method
referred to will be of direct service, but where the lead is greater than
0.6 inch the following tables can be used to great advantage as these
give at once the settings of dividing head and vertical milling attach-
ment for leads from 0.6 inch to 6 inches.
These tables give all the information necessary and it only remains
for the milling machine operator to select the lead of the desired cam
from the tables and set up for the corresponding change gears and
angles.
In setting the vertical milling attachment read the angle direct
from the dial. Example: if the angle given in the table is 395
degrees, set the spindle 39^ degrees from, its vertical position.
Fig. 5. — ^ Milling Cams
In setting the dividing head, subtract the angle in the table from
90 degrees. The difference represents the angle to which the dividing
head spindle must be raised from the horizontal position.
Example : The angle given in the table is 39I degrees. 90 degrees —
39^ degrees equals 50^ degrees.
Set the dividing head spindle 50I degrees up from the horizontal
position. This angle is read direct from the dial. The set up is
shown in Fig. 5.
The tables may of course be used in connection with the cutting of
any other similar cams.
156
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IS*
5
960
40
44
48
72
10
5-465
44
^t
64
7238^
5
71s
40
48
6a
72
39*
5
96s
40
48
56
72
23
5-470
72
48
24
6413.
5
720
4°
44
56
72
36
5
970
44
40
48
72
35*
5-475
64
48
32
72 225
5
725
86
44
24
72
28*
5
975
56
44
48
100
12
5-480
48
56
64
7244
5
730
48
64
44
56
13*
5
980
44
48
56
72
33
5-485
72
48
32
6443
5
735
48
64
56
72
10*
5
985
40
56
64
72
19*
5 -490
86
44
24
6441I
5
740
44
56
64
86
II
"5
990
72
48
32
64
37,
S-495
44
48
56
86 23
5-745
72
48
32
64
40
5-995
44
48
64
86
28*
i68
MILLING AND MILLING CUTTERS
PLAIN AND DIFFERENTIAL INDEXING ON BROWN &
SHARPE MILLING MACHINES
The general arrangement of the universal dividing head is illus-
trated in Figs. 1,2, and 3. As indicated by the diagrammatic sketch
Fig. 2, the worm wheel A is secured to the main spindle of the spiral
head and rotated by means of the worm shaft and single-threaded
worm B. The index plate (having rows of equally spaced holes)
remains stationary during the dividing operation, and is fitted with
adjustable sector arms which obviate the necessity of counting the
number of holes tlirough which the index crank requires to be moved
each time a division is made on the surface of the work. The stan-
FiG. I. — BrowTi & Sharpe Dividing Head Arranged for
Differential Indexing
dard ratio between the worm B and the worm wheel A is i : 40; and
to find the movement of the index crank for any required division,
the following formula is employed: The movement of the index
crank = ^ where N is the number of equal divisions required.
N
Example: Let it be required to divide the circumference of a piece
of work into 48 equal parts.
The movement of the index crank for each division = ^ = ^ revohi-
^ ^ 48 6
lions. ^
An index plate having a row of 18 holes would be chosen, and the
sector arms set to limit the movement of the index crank to 15 spaces
5 ^ 15.
for
18
General Principle of Differential Indexing
The number of equal divisions which may be obtained by simple
indexing (with the index plates usually provided by milling-machine
makers) is strictly limited, and does not meet all the requirements
called for in practice.
Differential indexing provides the most convenient way of over-
coming this difSculty, this method being simpler than compound
PLAIN AND DIFFERENTIAL INDEXING
169
indexing. In the differential system the dividing operation is per-
formed as in simple indexing, the only difference being that the index
plate instead of remaining stationary during the process of indexing,
is made to move relatively to the index crank, being connected to the
main spindle of the spiral head by a set of change gears, which may
be arranged to give either a positive or negative movement to the
Fig. 2
Worm Wheel,
40 Teeth
Single Thread
Worm
Main Spindle
Index Plate
Index Crank '
Fig. 3
index plate; whichever is found necessary to determine the actual
motion which must be given to the index crank in order to satisfy the
formula given above for simple indexing: Actual movement of the
index crank = — - •
N
The two views in Fig. i and the diagram. Fig. 3, will serve to give
an idea of the arrangement of the gearing, which is adopted in dif-
ferential indexing.
I70 MILLING AND MILLING CUTTERS
For any movement of the index crank the motion is transmitted to
the index plate (which is free to rotate on the worm shaft) as follows:
The index crank drives through the worm shaft and worm B to the
worm wheel /I, which in turn transmits the motion through the change
gears, spiral gears and equal gears, the last of which is connected
directly to the index plate. The last pair of gears being equal and
driven through equal spiral gears, whatever number of revolutions
are given to the gear £, the index plate will make the same number.
It is therefore convenient to consider the revolutions of the gear E,
as the revolutions of the index plate in all calculations.
To illustrate the influence of the gearing on the index plate and
indexing operation, consider the following example: Required to
index for 107 divisions:
If we use the plate having 20 holes and move 8 holes per division,
as in simple indexing for 100 divisions, 100 moves will of course be
required to rotate the worm 40 turns, which in turn rotates the
spindle once. If now we make 107 moves with the index plate fixed
8
as in simple indexing, we will obtain 107 X — = 42.8 revolutions of
20
the worm, which is 2.8 in excess of what is required. Therefore the
index plate must be geared so that it will move back 2.8 turns while
the spindle is revolving once; that is, the ratio of the gearing must be
2.8 to I.
2^
I
2
x^
I
2.8
2
X
20
=
20
= 56
40
^x3f
I 32
= 64
32
Then— = ^ X —and the gears will be 64 and 56 for the spindle
I 40 32
and first gear on stud, and 40 and 32 for the worm and second gear on
stud, as shown in Fig. i. As compound gears are used, but' one idler is
required to cause the index plate to move in a direction opposite to that
of the crank. For this purpose an idler having 24 teeth is employed.
Formula for Finding the Gear Ratio
A simple formula for the determination of the gear ratio necessary
to rotate the index plate as required for any given number of teeth
is derived as follows:
Let N equal the number of divisions required to be indexed.
Let n equal some number either greater or smaller than A'', which
can be obtained directly by simple indexing.
Let ^ equal the index setting; that is the setting of the sector
n
arms for each movement of the index crank;
Then n — N X— equals the gear ratio.
n
PLAIN AND DIFFERENTIAL INDEXING 171
If the number chosen for n is greater than the number of divisions
required (iV) the index plate must be geared to have a positive motion,
that is to rotate in the same direction as the index crank. If the
number n is less than N the index plate is geared to have a negative
motion, that is, to rotate in opposite direction to the crank.
Application of the Formula
Suppose we wish to obtain 63 divisions: choose any number for
n which may be obtained by simple indexing, say 60, then
{n - iV) = (60 - 63) = - 3
This number (— 3) when multiplied by the value of the index setting
will give the gear ratio. The index setting equals — , equals — , then
n 60
{n - N)^= - 3 X^ = -— or ^ as the gear ratio.
n 60 30 I
We can therefore use gears of 48 and 24 teeth, the 48 gear being the
driver and the 24 gear the follower; that is, the 48 gear being on
the spindle and the 24 gear on the worm. As n is smaller than N
the idlers are arranged to give a negative movement to the index plate.
The index setting is found above as — which equals i5 or - • We
n 60 3
can thus use the 39 hole circle in the index plate and set the sector
for 26 holes, this giving the setting as — or - ; that is, we set the sec-
39 3
tor and index pin exactly the same as for simple indexing of 60
divisions.
The tables on the following pages give the dividing head gears for
indexing all numbers up to 730.
172
MILLING AND MILLING CUTTERS
1
1
"o
1
No. I Hole
-a
a
C/2
Idlers
•>
2
d
0
Si
ui
S
^-.
4J
rS
fe
u
Hx
fl
0^
3
c
w
ffi
S
3
1
:i
0
l-i
^1
11
0
d
6
^
a
^
0
b
C/3
0
^
Z
2
Any
20
3
39
13H
4
Any
10
5
Any
8
6
39
6ff
7
49
5lf
8
Any
5
9
27
4-lf
10
Any
4
II
33
3II
12
39
13
39
3^
14
49
2ff
15
39
2ff
16
20
2it
17
17
2tV
18
27
'Y
19
19
2tV
20
Any
2
21
21
iff
22
33
23
23
ill
24
39
I2I
25
20
26
39
1-9
27
27
l-y
28
49
iii
29
29
I^¥
30
39
I^f
31
31
I^
32
20
I^
33
33
1,\
34
17
itV
35
49
itV
36
27
lir
37
37
• I3V
38
19
^¥
39
39
I3V
40
Any
I
41
41
It
42
21
M
PLAIN AND DIFFERENTIAL INDEXING 173
s
No. I Hole
Idlers
;|
V
>
"o
s
g
?3
^
Q
1
0
0
0^
0
-0
'5,
00
§
<0
1
3
X
11
s
12 c^
8§
2
d
6
:^
^
2
0
&H
cJ^°
0
:z;
^
43
43
40
44
33
ft
45
27
It
46
23
ft
47
47
ij
48
18
If
49
49
¥9
50
20
M
51
17
T7
24
48
24
44
52
39
§¥
53
49
If
56
40
24
72
54
27
n
55
33
11
56
49
If
57
21
if
56
40
24
44
58
29
I9
59
39
If
48
32
44
60
39
2 6
^9
61
39
If
48
32
24
44
62
31
M
63
39
^6.
24
48
24
44
64
16
T§
65
39
11
66
33
ft
67
21
28
48
44
68
17
T7
69
20
i^
40
56
24
44
70
49
If
71
18
it
72
40
24
72
27
if
73
21
i!
28
48
24
44
74
37
If
75
15
rJ
76
19
T9
77
20
20
32
48
44
78
39
ft
79
20
it
48
24
44
80
20
it
81
20
2^
48
24
24
44
82
41
If
83
20
^0
32
48
24
44
174
MILLING AND MILLING CUTTERS
1
No. I Hole
Idlers
'>
•0 ■
s
g
t.
T3
Q
i
3
^0
in
-%
0
1
u
!:e
§
^73
3
0
X
W
g
X
. G
>-
•" 3
0 C
>-
"
N
3
-o
0 1—1
UiO
u '^
S
6
6
^
c
12;
0
S
0
^
^
84
21
i^
85
17
8
86
43
^3
87
15
tV
40
24
24
44
88
33
if
89
18
t\
72
32
44
90
27
1}
91
39
U
24
48
24
44
92
23
M
93
18
tV
24
32
24
44
94
47
¥
95
19
tV
96
21
^\
28
32
24
44
97
20
^^^
40
48
44
98
49
II
99
20
2V
56
28
40
32
TOO
20
A
lOI
20
/o
72
24
40
'48
24
102
20
#0
40
32
24
44
103
20
^
40
48
24
44
104
39
¥
105
21
106
43
if
86
24
24
48
107
20
A
40
56
32
64
24
108
27
^f
109
16
fl
32
28
24
44
IIO
33
III
39
is.
24
72
32
112
39
II
24
64
44
113
39
"H
24
56
44
114
39
if
24
48
44
115
23
A
116
29
'4
117
39
If
24
24
56
118
39
13
•39
48
32
44
119
39
if
72
24
44
120
39
if
121
39
¥¥
72
24
24
44
122
39
tI
48
32
24
44
123
39
if
24
24
24
44
124
31
M
PLAIN AND DIFFERENTIAL INDEXING 175
0
!2
No. I Hole
Idlers
"o
g
c
u
-3
Q
4)
i
g
0
6
c
•0
a
p
?=
b
^^
'5.
C/3
■%
S
^
t-.
c
0
C-H
3
§
W
X
"s
S
°-g
i-t
^B
§C
tH
"
N
3
'^
^'~'
6
.b^
0 °
0
6
6
^
C
z
0
E
C/2
0
^
:2;
125
39
fl
24
40
24
44
126
39
il
24
48
24
44
127
39
M
24
56
24
44
128
16
A
129
39
ii
24
72
24
44
130
39
-y-
131
20
#
40
28
44
132
33
V
^33
21
A
24
48
44
134
21
.^r
28
48
44
13s
27
^
136
17
tV
137
21
/t
28
24
56
138
21
A
56
32
44
139
21
2*^1
56
32
48
24
140
49
-it
141
18
T%
48
40
44
142
21
A
56
32
24
44
143
21
A
28
24
24
• 44
144
18
T§
145
29
.>
146
21
^J
28
48
24
44
147
21
21
24
48
24
' 44
148
37
^.^
149
21
2^1
28
72
24
44
150
15
^^
151
20
2'0
32
72
44
152
19
A
153
20
2%
32
56
44
154
20
*
32
48
44
155
3i
A
156
39
i^
157.
20
io-
32
24
56
158
20
h
48 •
24
44
159
20
¥
64
32
56
28
160
20
^v
161
20
#
64
32
56
28
24
162
20
^^
48
24
24
44
163
20
5
20
32
24
24
44
164
41
H
165
33
33
176
MILLING AND MILLING CUTTERS
•s
No. I
Hole
Idlers
•>
"o
g
c
b
5
0
CJ
s
0
S
c
-^
p
^
1
^-^
1
u
0
3
0 a
c
0
X
p
Ci-I
u
^ °
w
6
6
J^
°
^
0
E
c^
0
Z
^
166
20
2^0
32
48
24
44
167
20
/o
32
56
24
44
168
21
¥
169
20
/o
32
72
24
44
170
17
17
171
21
^1
56
40
24
44
172
43
V
173
18
1%
72
56
32
64
174
18
T%
24
32
56
175
18
t\
72
40
32
64
176
18
t\
72
24
24
64
177
18
1%-
72
48
24
178
18
T%
72
32
44
179
18
t\
72
24
48
32
180
18
t\
181
18
A
72
24
48
32
24
182
18
A
72
32
24
44
183
18
A
48
32
24
44
184
23
iV
185
37
A
186
18
t\
48
64
24
44
187,
18
t\
72
48
24
56
24
188*
47
i?-
189
18
A
32
64
24
44
190
19
t\
191
20
2%
40
72
24
192
20
.%
40
64
44
193
20
/o
40
56
44
194
20
¥
40
48
44
195
39
A
196
49
H
197
20
/o
40
24
56
198
20
/o
56
28.
40
32
199
20
.%
100
40
64
32
200
20
2%
201
20
/o
72
24
40
24
24
202
20
*
72
24
• 40
48
24
203
20
Y%
40
24
24
44
204
20
♦
40
32
24
44
205
41
^h
206
20
2%
40
48
24
44
PLAIN AND DIFFERENTIAL INDEXING 177
§
No. ]
Hole
Idlers
*tn
'?
•^
s
c
u
'V
5
V
c
s
0
<u
3
•0
1^
p
^
c3
^^
1
0
-3
1
s
4J
. a
§
fl
3
0 3
!3
3
^
s
ucn
aj °
S
d
d
^
c
^^
0
E
0
^
^
207
20
^
40
56
24
44
208
20
#
40
64
24
44
209
20
¥
40
72
24
44
210
21
^\
211
16
A
64
28
44
212
43
:r\
86
24
24
48
213
27
iV
72
40
44
214
20
#
40
56
32
64
24
215
43
^/
216
27
h
217
21
A
48
64
24
44
218
16
A
64
56
24
44
219
21
^>
28
48
24
44
220
33
♦
221
17
TT
24
24
56
222
18
A
24
72
44
223
43
¥
86
48
24
64
24
224
18
*
24
64
44
225
27
fy
24
40
24
44
226
18
t\
24
56
44
227
49
¥
56
64
28
72
228
18
¥
24
48
44
229
18
tV
24
44
48
230
23
¥
231
18
*
32
48
44
232
29
2%
^i2>
18
-'^
48
56
44
234
18
j\
24
24
56
235
47
iS
236
18
t\
48
32
44
237
18
1%
48
24
44
238
18
A
72
24
44
239
18
A
72
24
64
32
240
18
tV
241
18
♦
72
24
64
32
24
242
18
A
72
24
24
44
243
18
A
64
32
24
44
244
18
T^^
48
32
24
44
245
49
A
?46
18
tV
24
24
24
44
247
18
t\
48
56
24
44
i7«
MILLING AND MILLING CUTTERS
.2
"o
g
No. I
Hole
Ji
^
Idlers
'>
p
S
c
0
0
u
a
•S
u
X
0
o*-i
u
4)
C/3
c
0
ni
'0
K
6
"o
W
N
6
1
c
^
0
S
c^
0
^
Z
248
31
A
249
18
♦
32
48
24
44
250
18
A
24
40
24
44
251
18
t\
48
44
32
64
24
252
18
♦
24
48
24
44
253
33
¥
24
40
56
254
18
tV
24
56
24
44
255
18
♦
48
40
24
72
24
256
18
A
24
64
24
44
257
49
^
56
48
28
64
24
258
43
^^
32
64
24
44
259
21
ih
24
72
44
260
39
♦
261
29
/^
48
64
24
72
262
20
2^^
40
28
44
263
49
^^
56
64
28
72
24
264
33
3%
265
21
A
56
40
24
72
266
21
*
32
64
44
267
27
^
72
32
44
268
21
A
28
48
44
269
20
64
32
40
28
24
270
27
271
21
A
56
72
24
272
21
♦
56
64
24
273
21
A
24
24
56
274
21
2\
56
48
44
275
21
■2^T
56
40
44
276
21
Y^T
56
32
44
277
21
/r
56
24
44
278
21
A
56
32
48
24
279
27
oV
24
32
24
44
280
49
iV
•281
21
^T
72
24
56
24
24
282
43
86
24
24
56
283
21
A
56
24
24
44
284
21
?T
56
32
24
44
285
21
A
56
40
24
44
286
21
^^
56
48
24
44
287
21
/t
24
24
24
44
288
21
A
28
32
24
44
PLAIN AND DIFFERENTIAL INDEXING 179
§
No.
I Hole
Idlers
'53
'>
"o
s
a
^^
n3
s
0
S
S
0
2
C
-z
"S
3
^
^^
*cf
"o
-B
1
s
3
1
Ol-H
§
c3
^1
3
0
3
M
d
6
z
l-l
^
0
E
C^
0
^
^
289
21
#
56
72
24
44
290
29
A
291
15
'40
48
44
292
21
rr
28
48
24
44
293
15
T^3
48
32
40
56
294
21
A
24
48
24
44
295
15
A
48
32
44
296
37
aV
297
33
A
28
48
24
56
298
21
¥
28
72
24
44
299
23
A
24
24
56
300
15
t!^
301
43
^^
24
48
24
44
302
16
A
32
72
24
303
15
A
72
24
40
48
24
304
16
♦
24
48
44
305
IS
i\
48
32
24
44
306
15
♦
40
32
24
44
307
15
A
72
48
40
56
24
308
16
¥
32
48
44
309
15
¥
40
48
24
44
310
31
A
311
16
A
64
24
24
72
312
39
^V
3^3
16
A
32
28
56
314
16
1^6
32
24
56
315
16
T6
64
40
24
316
16
T^
64
32
44
317
16
TS
64
24
44
318
16
t\
56
28
48
24
319
29
2%
48
64
24
72
24
320
16
T6
321
16
?
72
24
64
24
24
322
23
2\
32
64
24
44
323
16
♦
64
24
24
44
324
16
*
64
32
24
44
325
16
t\
64
40
24
44
326
16
TS
32
24
24
44
327
16
^
32
28
24
44
328
41
A
329
16
tV
64
24
24
72
24
i8o
MILLING AND MILLING CUTTERS
1
No.
[ Hole
Idlers
i>
"o
g
fl
^
'a
Q
u
fl
S
0
S
a
"S
>
0
"0.
u
9)
o
a
3
;>
Si
-d
en
"o
"3
1
'0
-of
0
-1
if
§
M
3
?
Ct-t
S
.S<^
u °
aj
d
Q
^
eS
^
0
s
c^
0
^
^
330
33
sir
331
16
*
64
44
24
48
24
332
16
T^
32
48
24
44
333
18
l\
24
72
44
334
16
t\
32
56
24
44
335
33
j\
72
48
44
40
24
336
16
l\
32
64
24
44
337
43
^\
86
40
32
56
338
16
1%
32
72
24
44
339
18
V
24
56
44
340
17
tV
341
43
4%.
86
24
32
40
342
18
t\
32
64
44
343
15
l\
40
64
24
86
24
344
43
fs
345
iS
T%
24
40
56
346
18
^>
72
56
32
64
347
43
^3
86
24
32
40
24
348
18
If
24
32
56
349
18
tV
72
44
24
48
350
18
A
72
40
32
64
351
18
t\
24
24
56
352
18
A
72
24
24
64
353
18
A
72
56
24
354
18
^
72
48
24
355
18
rs
72
40
24
356
18
^s
72
32
24
357
18
i\
72
24
44
358
18
T%
n
32
48
24
359
43
tV
86
48
32
100
24
360
18
T8
361
19
t\
32
64
44
362
18
t\
72
28
56
32
24
363
18
t\
72
24
24
44
364
18
A
72
32
24
44
365
26
2%
32
48
24
56
366
18
A
48
32
24
44
367
18
T%
72
56
24
24
368
18
t\
72
24
24
64
24
369
41
A
32
56
28
64
370
37
/y
PLAIN AND DIFFERENTIAL INDEXING l8l
1
"0
s
No. I
Hole
Idlers
!>
g
'0
1
1
c
0
1-
-OT3
.S
1
1
11
t
si
0-2
6
d
ll
c
^
0
£
^
0
^
^
371
21
2\
32
56
24
64
372
18
tV
48
64
24
44
373
20
^
40
48
32
72
374
18
tV
72
64
32
56
24
375
18
T^
24
40
24
44
376
47
V
377
29
2^
24
24
56
378
18
A
32
64
24
44
379
20
^%
48
56
40
72
380
19
T9
381
18
t\
24
■
56
24
44
382
20
i~0
40
72
24
383
20
2\
40
681
44
384
20
2\
40
64
44
385
20
t^
32
48
44
386
20
^\
40
56
44
387
43
t\
32
56
28
64
388
20
-io
40
48
44
389
20
2/
40
44
56
390
39
¥
391
20
2^0
48
24
40
72
392
49
4^
393
20
/o
40
28
44
394
20.
2S
40
24
56
395
20
■^
64
32
44
396
20
?^
56
28
40
32
397
20
2/
64
24
40
32
398
20
2^0
100
40
64
32
399
21
¥
32
64
44
400
20
-h
401
21
i-T
56
32
24
76 1
402
21
2T
28
48
44
.
403
20
♦
64
24
40
32
24
404
20
♦
72
24
40
48
24
405
20
2^0
64
32
24
44
406
20
#
40
24
24
44
407
20
2%
40
28
24
44
408
20
^^0
40
32
24
44
409
20
2^0
40
24
32
48
24
410
41
t\
Note. Special gears in this and following tables are 46, 47, 52, 58,
68, 70, 76, 84. 1 Special gear.
l82
MILLING AND MILLING CUTTERS
o
'53
g
1
g
No. 1
Hole
■a
in
%
Idlers
1
1
1
S
3
"^"B
o^-"
s
12 00
0 c
%
6
6
"A
c
!2;
0
E
^
0
^
^
411
21
^T
28
24
56
412
20
2V
40
48
24
44
413
21
¥
48
32
44
414
21
56
32
44
415
20
?o
32
48
24
44
416
20
2V
40
64
24
44
417
21
^\
56
32
48
24
418
20
-/o
40
72
24
44
419
33
¥
44
28
24
72
420
21
/t
421
20
^0
48-
56
40
72
24
422
20
2^7
40
44
32
64
24
423
21
A
72
24
56
48
24
424
43
t\
86
24
24
48
425
21
2T
72
48
56
40
24
426
21
^J
56
32
24
44
427
20
2^U
40
48
32
72
24
428
20
2V
40
56
32
64
24
429
21
A
28
24
24
44
430
43
/it
431
21
-h
72
44
28
48
24
432
20
2%-
40
56
28
64
24
433
20
1^^
40
44
24
72
24
434
21
A
48
64
24
44
435
21
2T
28
40
24
44
436
20
i-.
40
48
24
72
24
437
23
-h
32
64
44
438
21
A
28
48
24
44
439
43
¥
86
24
24
72
24
440
33
3^3
441
21
ii
32
64
24
44
. 442
20
2%
40
56
24
72
24
443
20
2V
40
48
24
86
24
444
21
^T
56
48
24
64
24
445
33
3\
64
32
44
40
24
446
33
-h
44
24
24
48
447
21
A
28
72
24
44
448
20
2^0
40
64
24
72
24
449
33
A
64
32
44
72
24
450
33
3V
44
40
24
32
PLAIN AND DIFFERENTIAL INDEXING
^83
1
"0
No. I
Hole
Idlers
*>
p
c
t
"^
Ji
a
jj.
0
0
"a
_o
lU
0
H
3
c3
•-H
CO
"0
-3
x^
'0
H X
c
0
0^
3
c
0
K
W
6
3
11
cS
tB,
c
0 a
03
6
6
^
0
l-H
z
0
E
CA)
0
^
'^
451
33
3
3 3
24
24
24
44
452
33
FS
44
48
24
40
453
33
-h
44
52^
24
40
454
49
4\
56
64
28
72
455
49
-.^
28
40
32
64
456
21
^T
56
64
24
72
24
457
33
33
44
681
24
40
458
33
il
44
72
24
24
459
27
^'V
24
48
24
72
460
23
2T
461
33
3\
44
28
24
72
24
462
33
i.
32
64
24
44
463
21
-h
56
64
24
86
24
464
33
A
44
48
28
56
24
465
33
-h
44
24
24
100
24
460
49
4
4 9
56
48
28
64
467
33
A
44
48
32
72
24
468
39
3
31
28
48
24
56
469
49
¥
28
48
44
470
47
/r
471
49
/.
56
32
28
76 1
472
49
*V
56.
32
28
72
473
33
I3
48
64
32
72
24
474
49
l\
56
32
28
64
475
49
l\
56
40
28
48
476
49
t\
56
64
24
477
27
iV
24
48
24
56
478
49
¥
56
24
28
64
479
49
¥
56
32
28
44
480
49
tV
56
32
28
40
481
37
aV
24-
24
56
482
33
3\
44
56
24
72
24
483
49
^S
56
32
44
484
49
¥
56
24
28
32
48s
23
^/
46 1
24
24
100
24
486
27
-ii
32
56
28
64
487
39
-h
24
72
52^
44
488
33
~h
44
64
24
72
24
489
23
*
46^
58^
Z^
64
24
490
49
4V
Special gear.
1 84
MILLING AND MILLING CUTTERS
1
"o
No. I
Hole
Idlers
1
§
1
^2
1
0,
<u
0
3
a
a
1
1
2
°'§
tt2
C
0 c
M
<N
"2
01— '
utn
« °
s
d
6
z
a
^
0
E
0
^
1
491
33
A
44
681
24
72
24
492
41
A
28
48
24
56
493
29
^^9
32
64
24
72
494
39
3\
32
64
44
495
27
^
32
40
24
64
496
49
t\
56
24
28
32
24
497
49
-A
56
32
24
44
498
27
-ii
48
56
24
64
499
49
^9
56
24
28
48
24
500
49
.?%
56
32
28
40
24
501
49
^\
56
32
28
44
24
502
49
i-.
56
32
28
48
24
503
23
A
46^
64
32
86
24
504
49
?%
56
64
24
24
505
49
^\
56
40
28
48
24
506
49
t\
56
32
28
64
24
507
39
-h
24
24
56
508
49
?\
56
32
28
72
24
509
49
?*^
56
32
28
76 1
24
510
49
/^
56
40
28
64
24
511
49
t\
28
48
24
44
512
49
■^s
56
44
28
64
24
513
27
■i.
32
64
44
514
49
■i-.
56
48
28
64
24
515
27
iV
72
32
24
100
• 516
43
Tj
32
56
28
64
517
49
^/
56
48
28
72
24
518
49
t\
28
64
24
44
519
27
^
72
56
32
64
520
39
3V
521
27
2V
72
76 1
•48
64
522
29
■i^
48
64
24
72
523
27
V
72
681
48
64
524
27
iy
72
32
24
64
525
27
-ij
72
40
32
64
526
49
A
56
64
28
72
24
527
31
A
32
64
24
72
528
27
2V
72
24
24
64
529
27
/r
72
44
48
64
530
15
tV
24
56
32
64
Special gear.
PLAIN AND DIFFERENTIAL INDEXING
i8S
1
*©
^
No. I
Hole
Idlers
>
^o
is
1
rt'S
h
"I-
"o
"o
'0
?2
§
S 3
1^ c
0 3
0 c
\
"H
d
ii; 0
iri '=>
0
6
6
1
c
^
0
(i(
c^
0
^
^
531
27
ij
72
48
24
532
27
2T
72
32
48
64
533
27
21
72
32
48
56
534
27
V
72
32
44
535
27
-h
72
32
48
40
536
39
-h
52'
64
24
44
537
27
-h
72
28
56
32
538
29
^9
58^
56
24
72
539
49
V
28
48
24
56
24
540
27
2V
54T
39
¥
52^
56
32
48
24
542
39
¥
52^
44
32
64
24
543
27
2V
72
24
48
32
24
544
15
tV
40
56
24
64
545
15
T^3
32
44
24
64
546
39
3^^
32
64
24
44
547
27
^V
72
32
48
56
24
548
27
^
72
32
48
64
24
549
27
V
72
48
24
24
550
15
¥
32
40
24
64
551
29
2^
32
64
44
552
27
-h
72
24
24
64
24
553
49
?\
28
48
24
72
24
554
27
2\
72
56
48
64
24
555
15
¥
24
72
44
556
15
¥
24
44
40
64
557
15
tV
40
32
24
86
558
27
9
¥
48
64
24
44
559
39
3^
24
72
24
44
560
43
?\
86
40
32
64
561
27
-h
72
56
32
64
24
562
27
ii
72
44
24
64
24
563
29
¥
58 1
681
44
564
43
86
24
24
56
56s
15
tV
24
56
44
566
43
¥
86
24
24
44
5^Z
15
tV
32
44
40
64
568
15
tV
40
32
24
64
569
29
/^
58^
44
24
570
15
tV
32
64
44
1 Special gear.
i86
MILLING AND MILLING CUTTERS
.2
'o
s
No. I
Hole
—
Idlers
■>
'0
0
g
0
.1
'S-
(3
0
0
1
3
^3
Is
l-l
|l
11
H
H
6
6
'iZ,
d
^
0
plH
C/2
0
^ iz;
571
43
_3_
86
28
64
32
572
15
T5
40
28
24
64
573
15
tV
40
72
24
574
41
l\
32
64
24
44
575
15
tV
24
40
44
576
15
tV
40
64
24
577
43
A
86
32
64
44
24
578
15
¥
48
44
40
64
579
15
2%
40
56
44
580
29
VV
581
15
tV
48
32
40
76 1
582
15
2V
. 40
48
44
583
27
tV
72
64
24
86
24
584
15
tV
48
32
40
64
585
15
tV
24
24
56
586
15
^^
72
48
40
56
587
29
tV
58^
28
24
44
588
15
tV
40
32
44
589
15
tV
72
44
40
48
590
15
¥
48
32
44
591
15
¥
40
24
44
592
16
tV
24
72
44
593
15
tV
72
28
40
48
594
35
3¥
32
56
28
64
595
15
¥
72
24
44
596
15
¥
72
24
40
32
597
33
A
44
56
24
72
598
16
tV
64
S6
24
72
599
43
A
86
44
24
84
24
600
15
tV
601
29
^v
58^
56
48
72
24
602
43
A
32
64
24
44
603
15
tV
72
24
40
24
24
604
16
¥
32
72
24
605
15
tV
72
24
24
44
606
15
tV
72
24
40
48
24
607
15
tV
■ 72
28
40
48
24
608
16
A
32
64
44
609
15
tV
40
24
24
44
610
15
tV
48
32
24
44
Special gear.
PLAIN AND DIFFERENTIAL INDEXING 187
.1
"o
No. I
Hole
■a
No. 2
Hole
'>
1
3
1
0
1
L
0 fl
crj
c
0
0
M
6
E
6
^
C
"^
0
E!
0
^
^
611
15
¥
72
44
40
48
24
612
15
tV
40
32
24
44
613
16
tV
64
48
32
72
614
15
tV
72
48
40
56
24
615
15
tV
24
24
24
44
616
16
tV
32
48
44
617
33
3J
44
32
24
86
618
15
tV
40
48
24
44
619
16
T>
48
28
2>2
72
620
31
3^
621
15
T^T
40
56
24
44
622
16
tV
64
24
24
72
623
16
tV
64
24
24
681
624
16
iV
24
24
56
625
15
tV
24
40
24
44
626
16
tV
32
28
56
627
15
tV
40
72
24
44
628
16
tV
32
24
56
629
16
tV
64
44
24
630
16
tV
64
40
24
631
16
tV
64
28
56
72
632
16
tV
64
32
44
633
16
tV
64
28
44
634
16
tV
64
24
44
635
15
I^^
24
56
24
44
636
16
tV
56
28
48
24
637
49
1¥
24
24
56
63S
29
lj'9
48
64
24
72
24
639
33
A
44
28
32
64
640
16
tV
641
33
A
44
32
48
76 1
642
16
tV
72
24
64
24
24
643
16
V
64
28
56
24
24
644
49
¥
56
32
44
645
15
1^
24
72
24
44
646
16
tV
64
24
24
44
647
16
tV
64
28
24
44
648
16
^
64
32
24
44
649
33
3^
72
48
24
650
16
tV
64
40
24
44
Special gear.
MILLING AND MILLING CUTTERS
.2
No. I
Hole
No. 2
Hole
5
1
1
1
§
§
Ot3
d
c
0
1
B
3
i
01— 1
2
lg
8
d
d
^
£
^
0
E
0
^
^
651
16
tV
64
44
24
24
652
16
T6
32
24
24
44
653
33
s\
72
28
44
48
654
16
tV
64
56
24
44
655
16
^.
64
40
32
48
24
656
16
tV
24
24
24
44
657
18
tV
32
48
24
56
658
16
tV
64
24
24
72
24
659
16
tV
64
24
24
76 1
24
660
33
l\
661
16
tV
64
56
48
72
24
662
16
tV
64
44
24
48
24
663
17
tV
24
24
56
664
16
tV
32
48
24
44
665
49
?v
56
40
24
44
666
18
tV
24
72
44
667
16
tV
64
48
32
72
24
668
16
tV
32
56
24
44
669
33
¥
44
24
24
24
670
33
72
48
44
40
24
671
33
72
48
24
24
672
18
s
24
64
44
673
16
tV
48
44
32
72
24
674
33
A
72
56
44
48
24
675
33
A
44
40
24
24
676
16
tV
32
72
24
44
677
18
tV
48
32
24
86
678
18
tV
24
56
44
679
49
^%
28
44
24
40
680
17
tV
681
33
A
44
56
24
24
682
33
A
48
64
24
24
683
16
tV
32
86
24
44
684
18
tV
32
64
44
685
18
tV
24
56
48
40
686
15
tV
40
64
24
86
24
687
18
tV
24
44
48
688
16
tV
24
72
24
44
689
39
A
24
48
24
56
690
18
tV
24
40
56
Special gear.
PLAIN AND DIFFERENTIAL INDEXING 189
1
1
'6
'2
L
4^
1
§
c3
No. I
Hole
Idlers
1
§
i-i
a
Ox)
1
6
K
6
1
c
;?
0
E
C/2
0
i
i
691
18
tV
48
32
24
58^
692
18
tV
72
56
32
64
693
18
tV
32
48
44
694
17
tV
681
56
24
44
695
18
tV
72
24
24
100
696
18
tV
24
32
56
697
17
V
24
24
24
44
698
18
IV
72
44
24
48
699
18
¥
48
56
44
700
18
tV
72
40
32
64
701
17
tV
681
48
32
56
24
702
18
tV
24
24
S6
703
19
t\
24
72
44
704
18
tV
72
24
24
64
705
18
tV
48
40
44
706
18
V"
72
56
24
707
18
j\
72
52^
24
708
18
?
72
48
24
709
18
V
72
44
24
710
18
tV
72
40
24
711
18
tV
64
32
44
712
18
^>
72
32
24
713
18
¥
72
28
44
714
18
tV
72
24
44
715
18
tV
72
32
64
40
716
18
tV
72
28
56
32
717
18
tV
72
24
64
32
718
33
3T
44
58^
24
64
24
719
17
tV
68 1
52^
24
72
24
720
18
tV
721
21
¥
24
64
32
681
722
19
¥
32
64
44
723
18
tV
72
24
64
32
24
724
18
tV
72
28
56
32
24
725
18
tV
72
24
48
40
24
726
18
tV
72
24
24
44
727
18
tV
72
28
24
44
728
18
¥
72
32
24
44
729
18
tV
64
32
24
44
730
20
2V
32
48
24
56
Special gear.
igo
MILLING AND MILLING CUTTERS
J
M
«
fO
-+
>o
\n
J^
on
Ov
o
m
^
m
VO
t~-
oo Ov
o
N ro ^
M IH
w
<N
o
•^
Ov
t^
o
in Ov
I^
H
in
Ov
IN
VO
O t 00
t^ r^
o
0
o
o
M
w
rn
o
o
o
o
o
o
o
0
o
o
O O
o
o
o
o
o
O O
o
O
COO
M
<N
in
O ro
IH
r^
o m
in
M -+ VO
CO
V)
r^
rt)
M
r^
r^
•m-
on
r^
Ov
<n in
Ov
O
■+
O CO M
M
HI
w
O)
fi
■^
o
o
o
C
o
0
0
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o
o
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o
0
o
o
o
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O
o
O 0 O
r<-
vr,
00
n
m
m
ca
.R
m
o
00 M
m
VO
00
M
rt
vO Ov
IH
^
O Ov w
i^
8^
on
m t^
1^
^ 5
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o
o
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M
M
m
rO
m
■^1-
o
o
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o
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o
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O
o
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o
o
o
o
o
O 0
o
00
o
_o_P_P__
VO d '=}•
rf
no
IS
-.(-)
o
m
t-~
^
in
Ov
m t-~
M
m
Ov
IV,
VO
Rv s;
Rv
r^
?
M-
t-
n\
^
o
o
O
M
o
p<
rO
m
m
^
•^ ^
M-
I/)
o
o
O
o
o
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o
o
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o
o o
o
o
O
O
o
o o
O
o
6 6 6 ■
rN
M
M t^
o
VO
rn
Ov
in (s
00
m
w r- ^
VD
rn
m
<N I^
M r^
^
o
o
O
H
M
CO
ro
r'J
^ •*
m
in lo VO
o
o
o
o
O
O
o
o
O
o
o o
0
O
o
O
o
VO
_o_o_
_o
_o_
_.o_o_o_
„
„
,_,
H
r)
IS
(>l
■*
fi
Ov
VO
o
t^ Tj-
00
VO rn
O
r^
m
^0
o
o
N
(M
N ro
WJ
r*!
1-
■*
^
tt m
in VO VO
o
o
o
o
O
O
O
o
O
o
o o
o
O
o
O
o
O O
O
O
COO
rn
^o
OS
N
M
r^
o
Ov
M
in
00
M
o
m
VO Ov <N
M
rn
•^
oo
^
t^
o
fO VO
oo
t t^
VO Ov <N
o
o
o
M
M
Ot
M
r-J
■^
■*
m
VO
o
o
o
o
o
o
o
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o
o
o o
o
O
O
O
O
o o
O
O
o o o
in
rT)
^
m
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w
VO
^
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M
"t
VO Ov
0)
Ti-
t^ O. r.
o>
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o>
o5 w
r^
o
o
O
CN
M
rn
m
i/>
r^ r^ t^
o
o
o
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o
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o
o
o
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o
o
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o
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O
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O O O
lO
o
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T1-
Ov
Cv
r^,
00
fn oo
m
(^
<s
r^
M
I^ (N
j^
IH
VO H VO
T)-
ro
r^
t^
J^ HI
C)
o
o
M
w
M
r'i
fj
"O -^
t^
t->. !>. 00
o
0
O
o
_o_
_o_
o
o
o o
O
o
O
O
o
_<^-__o_
r-
_o_
o o o
00 Ov 00
o
„
„
IH
m
m
'T <
m
in
m
^
t^
•* 00
Ov
O -i-
00
Ov
VO o
t
01
o
o
M
M
C-l
M
c<.
Uj
t^
I^
d
o
o
o
o
O
o
O
O
o
o o
O
O
O
O
o
o o
O
o
6 6 6
o
^
Oi
tT
^
m
on
m
on
rn f-
r<
r^
N
1^
M
VO w
%
o
in
Tt
r^
=§
N-1
^
t-» n
o
M
(N
tn
^0
■*
•* in
vO
vO
VO
r^
r- CO
CXJ
o
o
o
o
o
o
O
o
O
o
o o
O
o
o
o
O
O O
o
o
O
<s
Tt
M
r^
o
VO
(V)
CO ^
a
vO
o.
R
A
^
r^
r> r-
00 Ov
o
M
r«
Tf
m in
VO
r-
t^
ou
Ov
d
o
o
o
O
O
O
0
o
O
O 0
o
o
O
o
O
0 o
o
s
^
R
R
R
^
R
g
R
g
R R
R
R
R
g
R
R R
O
in
6
in
0
6
O m
o
1^
d
o
o
o
o
O
o
o
d
o
n o
o
o
o
o
o
O O
,^
rs
^
M
i^
■^
Ov o
r-1
in
H
t^
o
oo M
Ov
^
0\
rl-
o
M
N
ro
-^
m
t^
(JJ
d
o
o
o
O
O
o
o
o
0
o o
O
o
o
o
o
O
tJ->
M
o
(N
t^
fn
00
o
in
i-v VO
M
t^
rn
CO
^~
f^
o
M
M
0)
M
Kj
f^
l-~
o
o
o
o
O
O
o
o
o
O
o o
O
o
O
o
o
00
vO
in
m
„
Ov
en
o
■^
(N
w Ov
^^
o
'^
ri
t^ m
Ov
I^
■* O
M
o
M
c>
■ll
1^
o
o
o
o
o
O
o
o
o
o
O O
O
o
o
0
n
in
o
m
n
in
o
m
o
;c R
in
n
in
r^
t^
VO
o
on
m
\o
i^
rn
w
o
M
(N
<n
to
■*
m
o
o
O
o
O
o
O
O
o
o
o o
O
o
o
o
r^
o
r^
en
n
o
rn O
VO
m
OO
^
M
o
M
Ol
^
VU
o
o
O
o
o
o
O
O
o
o
o o
o
O
o
M
fO
■*
vO
r-
00
Ov
o
M M
rn
t
in
VO
r-
00 o.
o
M
N
INDEXING ANGLES
191
i
>o \o
t^
00
Ov 0
CO
Ov 0
w <N CO 'd- 10 VO
t^ CO
0
(N to
to to to to to to to
to
to 'T
T 't "T '^ ^ ^
^ T
s^
"^
^ 00 <N
VO M lO 0> to r- HI
"wo"
Ov to
t^ M 10 0 't 00
>0 r- t^ 00 00 CO
(N VO
c-
M
M M
f-1 to to to ^ ■* >o
VO VO
0 0
M to
r^
Ov M
to lo t- ov M to 10
t^
0> H
CO >o t^ Oi M CO
■*
10
XT, VO
VO VO VO VO t^ r^ t-
t- 00
00 00 00 00 Ov Ov
0 s
6 d
d
d
d d
d d d d d d d
d
d d
6 6 6 6 6 6
d d
M "^
>o
t^
0 to
VO Ov M •* r^ 0 <N
VO
CO H
to -o Ov <N rt r-
Tj-
!>. 00
00 (N r/, ,-j. VO t^
Ov H
<N to ■* VO t^ 00
r^
0
H to
VO 00 0 M Tl- t- 00
1>- Ov M to 10 t^
■*
>r> U-1
10
VO VO
vO vO t^ t-- t^ t^ r^
CO
c» 00
CO CO Ov 0 Ov Ov
d d
d
d
d d
6 6 6 6 6 6 6
d
d d
6 6 6 6 6 6
't r-
Oi
P4
5f:
t^ Ov
Ov <N •* f- 0 <N lO
r^
0 IN
10 CO
f^
00 0
VO
0 t t^ 0 '^ t- 0
S
r- 0
to VO
VO r^
•*
10 0
VO
VO
VO v5
rl tS[ t^ t^ (5 00 00
00
0> Ov
0 Ov
d d
d
_o_
d d
d d 6 6 6 6 6
d
d d
d d
00 w
10
Ov
to t^
M lo 0. to t^ 0 ■*
00
<N 0
0 •:)-
00
t^ M
VO 0 •* OV to CO <N
VO
0 ro
to
c»
0 to
10 00 0 t^ vc t^ 0
r^ r^ 00 CO CO 00 0>
VO r^
"+
VO VO
0
0
t^ r-
o>
Ov Ov
d d
d
d
d d
6 6 6 6 6 6 6
_d_
d d
0 0
to
Ov
VO <N
0> VO (N CO '^t M 1--
to
M vO
t^
to 0
^ 0 vO 1-1 r^ to CO
^
0
■:*• 0
o>
-t VO
Ov c, ^ t^ Ov « Tl-
t^
rO
0 VD
0
r^
t^ t^
t^ 00 00 00 00 Ov a.
Ov
d d
d
d
d d
6 6 6 6 6 6 6
d_
r- r^
t^
00
CO 00
CO r^ Ov C 0 0
o>
VO
<o 0
I^ .^t M OD 10 to
f^
r~ 0
00 M
to 0 0> M -+ t^
to
VO t^
t^
r^
t^ 00
00 00 00 Ov 0> Ov
d d
d
d
d d
6 6 6 6 6 6
^ >
\
10 00
H
.rf
r- 0
to VO
r^ r-
00
00
00 0
0 Ov
>-Y
X
rO
>/-; 00
Tt
r^ 0
00 0
\
ro
r^ r^
00
00
0 s
« r\
\
d d
d
d
d d
d d
J--C---,
)
ly-> t-^
0
c^
10 i^
~
1
to
10 r^
\
/
<0
00 00
d d
d
a
d
d d
V
y
M 0
0
10
Oi
0 "S
VO
N
00 00
d d
d
Ov
d
0^ 0
\n to
"
0. VD
d d
H
•oper
r all
tion.
sec.
the
'1
<
-0 ■-
I-)
a ° S M -S
E 3
Ph
X
(2^
lllil
Q
h-)
^ 0
2
0
<3
culations when obta
grees, minutes or sec
e will readily show its
one of 31 deg., 17 nn
ds = 112,631. One
to seconds = 32,400.
*3 M-i
5 .
0
^
0
VO
to
" 8
HH
"d-S &•== §1
II
^ >
s many
either in
An exar
; indexed
gle to se
hich redu
5 1
d -
s
. pq
Ji a -B ,D S ^
S
The tab
dex for a
ree collec
The angl
educing 1
ank = 9 c
We. find
holes on t
places.
.S5 rt S
192
MILLING AND MILLING CUTTERS
MILLING CUTTER, REAMER AND TAP FLUTES
The following tables give the number of teeth or flutes suitable
for milling in various types of cutters, reamers, taps, etc., and also
show the forms of fluting cutters used.
End Mills
Straight Teeth
Spiral Teeth
Dia. Mill
No. Teeth
Dia. Mill
No. Teeth
A to t\
f to I
I J to if
6
8
10
12
14
\ to h
T^eto if
I to li
if to I i
8
10
12
14
Shell End Mills-, Straight
Teeth
OR Spiral
Inserted Tooth Cutters, P. & W. Form
Dia. Mifl
No. Teeth
Dia. Cutter
No. Blades
4
10
5
12
6
16
7
18
il to I^
16
8
20
if to 2x^^
18
10
24
2|tO 3
20
12
28
Metal Slitting Cutters
Thickness
Pitch
Thickness
Pitch
i^
h
♦
Pr
\
^
¥
■jV
■s%
i
t
i
A
Screw Slotting Cutters
Cutters thinner than 3V cut ^ pitch,
Cutters -^ to ^ thick cut -^s pitch.
Cutters over ^^ thick cut 3^ pitch.
PLAIN MILLING CUTTERS
193
Plain Milling Cutters
Fluting Cutters
Dia. of Cutter
No. of Teeth
J
2 to 2!
18
\ ■
3 to 3I
4 to 5
5i to 6
6ito 8f
9 to 9I .
9J to 10
io| to 1 1
20
22
24
26
28
30
32
/
40° to 48°
Form of Cutter for Milling
Teeth in Plain Milling
Cutters.
Plain cutters of f-inch face and over are generally made with
spiral teeth. The 12-degree angle on side of fluting cutter gives
ample clearance for cutting spiral grooves with the 12-degree face
set on the center line of the work.
Side or Straddle Mills
Dia. of Cutter
No. of Teeth
-
aX^
2
16
\
2^
2f to 3i
34 to 4i
5 to5f
6 to6|
7 to7|
8 to8f
20
24
26
28
30
32
34
Angular Cutter for MilUng
Teeth in Straddle Milling
Cutters.
For milling teeth on periphery of straddle mills use angular cutter
with 60 degree angle at A; for milling teeth on sides of cutters use
70°, 75° or 80° cutter according to number of teeth in cutter to be
milled.
194
MILLING AND MILLING CUTTERS
Corner Rounding Cutters
Fluting Cutters
2i to 3i
3ito4
Angular Cutter for Milling
Teeth in Corner Round-
ing, Concave and Convex
Cutters.
Angular Cutters
Dia. of Cutter
No. of Teeth
1
fv
3
l8
20
22
B
/
\
Double Angle Cutters
Dia. of Cutter
No. of Teeth
2* to 3
22
Cutters for Spiral Mill;
Dia. of Cutters
2*
3
Cutter for Milling Teeth in
Angular Cutters, Double
Angle Cutters and Cut-
ters for Spiral Mills. To
cut Teeth on side A of
this Cutter use 6o° Cutter.
To cut side B use 7o°-75^
Cutter.
SCREW MACHINE TAPS
195
Hand Taps
Tap Fluting Cutter
Dia. of Tap
No. Flutes
(
With
3 Flutes in
4 Flutes in
5 Flutes in
6 Flutes in
7 Flutes in
8 Flutes in
With
3 Flutes in
4 Flutes in
5 Flutes in
6 Flutes in
7 Flutes in
8 Flutes in
In milHng
cutter the c
the tap.
^toif
l| to 2f
3 to 4
3 to 4 mm.
5 to 44 mm.
4
6
8
3
4
6
^
^--B—
J.
46 to 50 mm.
Taps
Machine Screw
2
No. Flutes
Dia. of Tap
X_?.
No. I to 7
No. 8 to 30
3
4
Tap,
Tap,
Tap,
Tap,
Tap,
Tap,
Tap,
Tap,
Tap,
Tap,
Tap,
Tap,
taps
atter r
B = 1 Dia.
B = J Dia.
B = If Dia.
B = H Dia.
B = 3% Dia.
B = 1 Dia.
E = 3^ Dia.
E = 1 Dia.
E = If Dia.
E = 11 Dia.
E = i^ Dia.
E = -h Dia.
w^ith the c
Tapper Taps
Dia. of Tap
No. Flutes
itoif
if to 2
2i
4
5
6
Tap
Tap
Tap
Machine or Nut
Taps
Tap
Tap
Dia. of Tap
No. Flutes
Tap
A to f\
f t0 2l
2|t0 3
33 to 4
4
5
6
7
Tap
Tap
Tap
Tap
Screw Machine Taps
Tap
Tap
Dia. of Tap
No. Flutes
onvex
i toii
lAt0 2
4
6
nus
t be centra
with
196
MILLING AND MILLING CUTTERS
Taper Pipe Taps
Tap Fluting Cutters
Dia. of Tap
No. of Flutes
ito 1
4
/-^ /K
1
4 or 5
(
1 \ \
I to ij
5
\Y\
2
7
2i
8
9
3
.__.
3^ to 4
II
/
Straight Pipe Taps
UJ
Dia. of Tap
No. of Flutes
B Ta
ito i
4
1 to I^
5
I^
6
2
7
Cutter A is a regular tap fluting cutter
2i
8
that may be used if preferred for fluting
3
9
any kind of tap in place of convex
3i
ID
cutter B.
Pipe Hobs
Dia. Hob
No.
Flutes
Dia. Hob
No.
Flutes
Dia. Hob
No.
Flutes
Hob Fluting
Cutter
Jtoi
6
I
12
3
28
A
i
8
li to I^
16
34
34
/ \
\
9
2
20
4
36
L.A
*
10
2i
24
4i
46
Sellers Hobs
Hob Taps
Dia. Hobs
No.
Flutes
Dia. Hob
No.
Flutes
Dia. Hob
No.
Flutes
■ to yV
6
if to 2\
12
\ to \
6
1
^ to ^
8
2% to 2|
14
A to 11
8
In fluting
H to li
10
3 to 4
16
1 toii
I f to 2
ID
12
hobs leave
land -^-^ inch
wide on top.
CUTTERS FOR FLUTING REAMERS
Shell Reamers
197
r-"
1
;2
Dia. of Reamer
"o
Dia. of Reamer
'o
Dia. of Reamer
"o
1
0
6
itof
6
|1 to li
10
23% to 2f
14
Mtof
8
iH to 2i
12
2f f to 4
16
Cutters for Fluting Reamers
Dia. of
R = Radius
Dia. of
R = Radius
Reamer
of Comer
Reamer
of Corner
\ ^
* to j\
0
I J toii
tV
ito i
^V
It's to 2i-
.\
/ \ \^
ito ^
3^
2T\t0 3
A
f to I
eV
A = Am't Cut-
A = Am't Cut
Dia. of
ting Edge is
Dia. of
ting Edge is
Ahead of
Reamer
Ahead of
Reamer
Center
Center
i
.Oil
l|
.066
i
.016
If
.076
1
.022
.027
2
2i
.087
.098
u
vv
4
■<^33
2*
.109
'A
^7<^
i
.038
2f
.120
/w \
I
.044
3
•131
1 \\ \
li
.055
( \\
V3/
The type of cutter shown may be used for all classes of reamers
except rose reamers.
MILLING AND MILLING CUTTERS
Rose Chucking Reamers
•X.
Use 75 Angular
Cutter for End.
Use 80 Angular
'Cutter for Flutes
Depth of Groove = H to % Dia.
"d
-d
(3
a
w
W
Dia. of Reamer
•oi2
6U
No. of
Flutes
Dia. of Reamer
No. of
Flutes
Z
^
ito i
6
3
if to 2
12
6
t to I
8
4
2i to 2 J
14
7
ijtoij
lO
5
2f to3
i6
8
Taper Reamers
Morse Taper
B. & S. Taper
Jarno Taper
<*H m
M-1 CO
V*, lA
No. of Taper
6.5
No. of Taper
6 3
No. of Taper
6 3
^t.
;^t^
Zu.
o to I
6
I to 5
6
2
4
2 to 4
8
6 to ID
8
3 to 4
6
5
ID
II to 12
10
5 to 10
8
6
14
13
12
II to 15
10
7
i6
14 to 16
14
16 to 18
12
16 to 18
16
19 to 20
14
Taper Pin Reamers
Locomotive Taper Reamers
No. of Reamer
No. of
Flutes
Dia. of Reamer
No. of Flutes
OOOO to 00
0 to 7
8 to 10
II to 14
4
6
8
10
i to i
i^toii
lA to if
ill to 2
6
8
10
12
HALF-ROUND KEYWAY
199
Center Reamers
diameter of straddle mill for fluting (3 flutes;
Outside
Outside
Size of Reamer
Dia. of
Size of Reamer
Dia. of
Cutter
Cutter
Y cut
2j
r cut
3l
r cut
2f
r cut
3f
r cut
3
i'' cut
4
f'' cut
3i
CUTTER KEYWAYS
Square Keyway
Dia. Hole, A
Width Key, W
Depth, D
Radius, R . . .
8 176
3
32
6^
.020
.030
*
•035
32
.040
ItWI
1
.050
iti
32
.060
I
.060
16
t\
.060
Half- Round Keyway
Dia. Hole, A.
l-f
H-H
FlT^
li-IlV
1^-2
2tV2tV
2^-3
Width, W....
i
^
i
t\
1
^^
i
Depth, D
tV
^^^
i
3^
1^
.V
i
200
STANDARD T-SLOT CUTTERS
Width of Slot
Diameter of
Width of Slot
Depth
Extreme Limit
A
Neck of Cutter
B
D
Inches
Inches
Inches
Inches
Inches
I
i2
h
A
A
A
1
fa
f
32
sV
T^
tV
1
— 1-
3^2
■^-g
h
tV
if
A
f
H
lA ,
f
li
1X^6
-|
I
X
If
I 1
-*
ItV
I
ft
If
lA
These cutters are made /a i^ch larger in diameter and ^\ inch
greater in thickness than the figures given, to allow for sharpening.
Largest Squares that can be Milled on Round Stock
Diam. of
Decimal g
ze of
Nearest
Diam. of
Decimal
Equiva-
lent
Size of
Nearest
Stock
lent ^
[juare
Fraction
Stock
Square
Fraction
i
.125
088
A-
l/lT
1-5625
1-105
i.V-
l\
.1875
133
i +
If
1.625
1. 149
13*^-
\
.250
177
•fi-
't*
1.6875
1. 193
It\ +
fe
•3125
221
i^ +
If
1-750
1-237
iM +
1
.375
265
il
lif
1. 8125
1.282
l/^
<^
.4375
309
I!~
If
1-875
1.326
Ifi-
i
.500
354
^1 _
64
lit
1-9375
1-370
If -
T%
•5625
398
11 +
2
2.000
I.414
lit +
«
.625
442
tV +
2tV
2.0625
1-458
iff +
ii
.6875
486
fi +
2f
2.125
1.502
i^ +
f
•750
530
2A
2.1875
1-547
Iff
Tt
.8125
574
f ¥ ~
2i
2.250
1-591
iff-
•875
619
1 -
St'V
2.3125
1-635
iff-
xf
•9375
663
M +
2f
2-375
1-679
iff +
I
1. 000
707
M +
2tV
2.4375
1-723
i|l +
ItV
1.0625 .
755
1 +
2i
2.500
1.768
ik +
li
1. 125
795
f i —
2t^
2.5625
1.813
Ik
It\
1-1875
840
II —
2f
2.625
1-856
if--
li
1.250
884
II —
2H
2.6S75
1.900
if^-
IT^^
1.3125
928
f f +
2f
2.750
1.944
iH +
If
1-375
972
fi- +
2H
2.8125
1.989
iff +
itV
1.4375 I
016
i^V +
2f
2.875
2.033
2h +
I^
1.500 I
061
ItV -
2H
3
2.9375
3.000
2.077
2.121
2i^-
SideofLar
gest Square = I
Ma.ofS
tockx.707
2f -
DISTANCE ON CIRCUMFERENCE
20I
Table of Divisions Corresponding to Given Circumferential
Distances
This table gives approximate number of divisions and distances
apart on circumference, corresponding to a known diameter of work.
It is useful in milling-machine work in cutting mills, saws, ratchets,
etc.
Distance on Circumference
Dia. of
Work
3^"
i^g"
r
^Y
X"
i%"
1"
iV
i"
1%"
r
ir
r
i"
ir
f
25
12
6
31
16
8
1
38
19
9
6
1^
44
22
II
7
5
^
50
25
13
8
6
1
63
31
16
10
8
6
f
75
38
19
13
9
8
6
1
88
44
22
15
II
9
7
6
I
100
50
25
17
13
10
8
7
6
i
126
63
31
21
16
13
10
9
8
7
6
J
150
75
3S
25
19
15
13
II
10
8
7
4
176
88
44
29
22
18
15
13
II
ID
9
8
7
6
2
200
100
50
34
25
20
17
14
12
II
10
9
8
7
6
i
226
113
56
38
28
23
19
16
14
13
II
ID
9
8
7
J
251
125
63
42
31
25
21
18
16
14
12
II
ID
9
8
1
277
138
69
46
35
28
23
20
17
15
14
13
12
10
9
3
302
151
75
50
38
30
25
22
19
17
J5
14
13
II
9
i
327
163
82
54
41
33
27
23
20
18
16
15
14
12
10
^
352
176
88
59
44
35
30
25
22
20
18
16
15
13
II
f
378
189
94
.63
47
38
31
27
24
21
19
17
16
14
12
4
402
201
100
67
50
40
34
29
25
22
20
18
17
IS
13
i
428
214
107
71
53
43
^^0
31
27
24
21
19
18
15
13
i
454
227
114
76
57
45
38
32
28
25
23
21
19
16
14
f
478
239
119
79
60
48
40
34
30
27
24
22
20
17
15
5
503
252
126
84
63
50
42
36
31
28
25
23
21
18
16
i
528
264
132
88
66
53
44
38
33
29
26
24
22
19
16
1
554
277
138
92
69
55
46
40
35
31
27
25
23
20
17
f
579
289
145
96
73
58
48
41
36
32
28
26
24
21
18
6
604
302
151
lOI
76
61
50
44
38
34
30
27
25
22
19
For example: A straddle mill, say, 5 inches in diameter, is to be
cut with teeth yV apart. Without a table of this kind the workman
will have to go to the trouble "of multiplying the diameter by 3.14^6
and then divide by j\ to find the number of teeth to set up for. In
the table, under j\ and opposite 5, he can find at once the number
of divisions, as 36. Where the table shows an odd number of teeth,
one more or less can, of course, be taken if it is important to have
even number of teeth.
202 MILLING AND MILLING CUTTERS
MILLING SIDE TEETH IN MILLING CUTTERS
The table gives the angle at which to set the dividing head of a
miller when milling the side teeth in milhng cutters.
Milling Side Teeth in Milling Cutters.
DiviorNG Head
Angle to set
Angle of
Cutter Used
No. of
Teeth
45°
50°
60°
65°
70°
75°
80°
85°
6
36° 08'
50° 55
62° 21
57° 08
81° 17
7
43° 36'
^X ^K
62° so
70° 22
72° 13
83° 42
8
32° 57'
54° 44
6i' 30
68° 39
74° 04
77 13
84° 52
9
32" 58
45° is'
61° 01'
66° 58'
72° 13
77° 00
81° 29
85° 47
lO
43° 24
52° 26'
65° 12'
70° 12'
74 40
78° 46
82° 38
86° 14
12
54° 44
61° 02'
70° 33
74° 23'
77° 52
81° 06
84° 09
87° 06
14
61° 12
66° 10'
73° 51'
77° oi'
79° 54
82° 35
85° 08
87° 35
i6
65° 32
69° 40'
76° 10'
78° 52'
81° 20
83° 37
8S°49
87° 55
i8
68" ,SQ
72° 13'
77° 52'
80° 13'
82° 23
84° 21
86° 19
88° IG
20
71 03
74 11'
79 II
81° 17'
83° 13
85° 00
86° 43
88° 22
22
72° 55
75° 44'
80° 14'
82° 08'
83 52
85° 29
87° 02
88° 31
24
74° 28
77° 00'
81° 06'
82° 49'
84° 24
8S°53
° 87° 18
88° 39
26
75° 44
78° 04'
81° 49'
83° 33'
84° 51
86° 12
87° 30
88° 45
28
76° 49
78° 58'
82° 26'
83° 53'
85° 14
86° 29
87° 42
88° SI
30
77° 44
79° 43'
82° 57'
84° 18'
85° 34
86° 44
87 51
88° 56
32
78° 32
80° 23'
83° 24'
84° 40'
8s°5i
86° 56
87° 59
89° 00
34
7Q° 14
80° =59'
83° 48'
85° 00'
86° 06
87° 08
88° 07
89° 04
^6
79° 51
81° 29'
84° 09'
8s°i7'
86° 19
87° 17
88° 13
89° 07
^8
80° 24
81° 58'
84° 29'
8s° 32'
86° 31
87° 26
88° 18
89° 09
40
80° S3
82° 22'
84° 45'
83° 46'
86° 42
87° 34
88° 24
89° 12
42
81° 20
82° 44'
85° 00'
8s° 58'
86°. 51
87° 41
88° 29
. 89° 14'
The table shows the angle to the nearest minute, but as an ordinary-
dividing head is not graduated to read in minutes, the nearest quarter
degree is taken.
SPEEDS FOR COLD SAWS
203
CUTTING SPEEDS FOR COLD SAW CUTTING-OFF
MACHINES
The table on page 204 shows the practice of the Brown & Sharpe
Mfg. Co. The semi-high speed still is used for soft steel but high
speed is recommended for cutting tool steel. A good lard cutting oil
is preferred though it can be dark colored and more impure than for
screw machines.
The experience of this company has led to the adoption of the saw
tooth shown herewith. This allows a slower speed and coarser feed
than finer teeth, and cuts stock more easily and quickly.
Space
-^"r*^A
Screw Diam. ' Thickness
16"to 18" 5/32"
22" 3/,j"
24" V32"
Section of Cut
Newton Machine Tool Works recommend a high speed and light
feed for steel low in carbon and manganese to keep the chip thin as
possible. Up to 35-point carbon use 6b to 65 feet per minute for
sohd blades. From 35 to 50-point carbon, 55 to 60 feet per minute
and less feed. Above 50-point carbon use inserted tooth saws. With
inserted tooth saws speeds can be from 50 to 80 feet per minute
on 50 to 70-point carbon, but only on heavy, rigid machines. For
cutting sprues in steel foundries a solid tooth saw with a speed
of 55 feet per minute and a feed of J to f inch per minute is recom-
mended. "*
The work should be flooded at all times with any good cutting
compound which does not rust. A good mixture is: whale oil, 9
quarts; pure lard oil, 2 gallons; sal soda, 15 pounds; and 40 gallons
of water.
The Tindel-Morris Co. give f inch per minute as a safe feed for
steel bars of 45-point carbon from 2 to 10 inches in diameter. The
speed of inserted tooth saws is given as 25 to 30 feet per minute, as
this, with a coarse feed, gives good results. This is with f inch spacing
between teeth. Liberal power is needed — a 36-inch saw requiring
from 10 to 15 horsepower.
204
MILLING AND MILLING CUTTERS
1
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(N <N CO CO '^ '^t- to 100 *0 ^^ t^OO
TURNING AND BORING
The accompanying table is a ready means of figuring machine time
on turned, bored or faced work.
The ordinary method employed is to ascertain the number of feet
in the circumference of the piece by multiplying the diameter in
inches by 3.1416 and dividing by 12. The next step consists of
dividing the length by the feed used, which gives the entire number of
revolutions the piece must make.
Constants for Cutting Time, in Minutes
Feed m
Inches
Cutting Speed
Two Cuts at
15 Feet
' 18 Feet
20 Feet
25 Feet
30 Feet
35 Feet
40 Feet
1-64 1-32
1.676
1.396
1-257
1.005
0.8378
0.7181
0.6281
1-32 1-16
0.8378
0.6981
0.6283
0.5027
0.4189
0.3590
0.3141
1-16 I- 8
0.4189
0.3491
0.3142
0.2513
0.2094
0.1795
0.1570
.1-8 1-4
0.2094
0.1745
0.1571
0.1257
0.1047
0.0898
0.078s
One Cut at
1-64
1. 117
0.9308
0.8378
0.6702
0.5585
0.4787
0.4189
1-32
0.5585
0.4654
0.4189
0.3351
0.2793
0.2394
0.2094
1-16
0.2792
0.2327
0.2094
0.1676
0.1396
0.1197
0.1047
I- 8
0.1396
0.1164
0.1047
0.0838
0.0698
0.0598
0.0524
I- 4
0.0698
0.0582
0.0524
0.0419
0.0349
0.0299
0.0262
Two Cuts at
45 Feet
50 Feet
60 Feet
70 Feet
80 Feet
90 Feet
100 Feet
1-64 1-32
0.5581
0.5027
0.4189
0.3590
0.3142
0.2793
0.2513
1-32 1-16
0.2793
0.2513
0.2094
0.1795
0.1571
0.1396
0.1257
1-16 I- 8
0.1396
0.1257
0.1047
0.0898
0.0785
0.0698
0.0628
1-8 1-4
0.0698
0.0683
0.0524
0.0449
0.0393
0.0349
0.0314
One Cut at
1-64
0.3723
0.3351
0.2793
0.2394
0.2094
0.1852
0.1676
1-32
0.1862
0.1676
0.1396
0.1197
0.1047
0.0931
0.0838
1-16
0.0931
0.0838
o.o6g8
0.0598
0.0524
0.0465
0.0419
I- 8
0.0465
0.0419
0.0349
0.0299
0.0262
0.0233
0.0209
1- 4
0.0233
0.0209
0.0175
0.0150
0.0131
0.0116
o.oios
Having the circumference in feet and the number of revolutions,
it is necessary to multiply them to find the entire number of feet
traveled. Dividing this result by the speed of cut in feet per minute
will give the actual cutting time in minutes.
The figuring is not comphcated in any way, but it has the disad-
vantage of taking too much time. It can be resolved into the follow-
ing formula:
205
2o6 TURNING AND BORING
Diameter X 3-Ui6 X length in inches ^ ^.^^ .^ ^,^^^^^^^
12 X speed X feed in inches
The known factors in the case can be resolved into a constant
which is directly dependent on the feed and speed; hence, a table
covering a wide range of speeds and feeds is necessary for their proper
use.
One part of the table gives constants for two cuts at e^-inch and
/o-inch feed, up to |-inch and i-inch feed, at any speed from 15 feet
to 100 feet per minute. The rest of the table gives constants for
one cut at g^-inch up to and including J-inch feed, also at any speed
from 15 feet to 100 feet per minute.
A typical computation is as follows :
A piece 4 inches in diameter, 10 inches long, is turned with two cuts
at xViiich and gVinch feed, each with a cutting speed of 20 feet per
minute. Diameter X length in inches X constant = time in min-
utes. 4 X 10 X 0.6283 = 26 minutes.
If, for the purpose of accuracy it is thought advisable, in connec-
tion with these two cuts, to run another cut over, the constant 0.6283
is added to a constant for the third feed used. If this feed is g^^-inch,
then we have 0.6283 + 0-8378 = 1.4661, the constant for three cuts,
one of xViiich, one of j^^-inch, and one of g^^j-inch feed.
Table Has Wide Application
There is hardly a combination of feeds and speeds that it is not
possible to secure by inspection from the table. By interpolation
an added number can be secured.
The table can be adapted, on account of its wide range, to the
kno^vn individual performance of any lathe or boring mill in the shop.
No slide rule or any special operations are necessary to secure the
desired results, merely a knowledge of multiplication.
For flange facing it is possible to use the table with the same ease
as for boring and turning by figuring on the main diameter.
Rotary Cutting Speed
An easy method of calculating the cutting speed of a lathe tool
or milling cutter is to divide the number of revolutions by 4 and
multiply by the diameter in inches. This gives the cutting speed
in feet per minute. Dividing 3.1416 by 12 gives .262 and .25 is very
close after allowing for belt slip.
Let D = diam. of work, cutter or boring bar.
N = revolutions per minute.
C = cutting speed in feet per minute..
4 D N
Lathe Tool Tests
In testing steels for lathe and similar tools it has become custo-
mary to use standard material, speeds, feeds and depth of cut. In
some cases tools are run until they break down, in others they are
CUTTING LUBRICANTS 207
passed if they stand up for a specified time. A 20-point carbon steel
is often selected and cuts I inch deep wdth jV to | inch feed at cut-
ting speeds of from 60 to 90 feet per minute.
The U. S. Navy Department specifies that a |-inch lathe tool
shall stand up for 20 minutes with a yVi^ch cut and j-^j-inch feed at
60 feet per minute without regrinding; the material must be at least
80,000-lb. , tensile, and 50,000-lb. elastic limit -with a 25 per cent,
elongation in 2 inches. The steel is annealed before the test.
Cutting Lubricants
Cast iron is usually worked dry, but when hard cast-iron gears are
to be cut, as ^^^th three cutters, the first cut through will work better
with strong soda water. It makes an objectionable mess, but the
work will be done faster and the cutters keep sharper longer than
with the dry process of cutting.
Brass and babbitt are usually cut dry, but to hand-ream brass and
babbitt is sometimes difficult if the reamer is a httle dull. Kerosene
and turpentine are used with good results. Cast iron can be hand-
reamed easily with tallow and graphite, mixed, and the hole will
be kept just the size of the reamer. Copper can be worked well v.dth
lard-oil and turpentine mixed.
In boring babbitt bushings and rod boxes in a lathe or boring mill,
it is very difficult to work the material dry as the chips have a great
tendency to roll around the tool and into a hard ball, tearing the
metal and making a rough ragged hole. In this case kerosene and
lard-oil mixed will work well.
Cheap oil is sometimes used as a lubricant for cutting, but soap
water or soda water is better for iron and steel shafting and with a
sharp tool and light finish cut the work will be smooth enough to
polish wthout filing.
Rawhide is a very peculiar substance to work, and to drill it with
a twist drill is a tedious job, as the flutes wiW clog and stick if run dry.
A cake of soap held against the drill will prevent all trouble and
sticking of drills. It is bad practice to use oil on rawhide as it injures
the fiber and loosens the glue. Drills should be run at very high
speed in rawhide to work well.
Turpentine is good in some cases where fitting is done, such as
scraping lay-out plates, or face plates. Oil will form a coating so
that marks cannot be seen plainly, but turpentine will prove bene-
ficial on this kind of work if used freely. The marks can be seen
plainly, and the work is a great deal easier to scrape than with an
oil surface, as the oil glazes over the surface and makes it hard to
start a tool.
GRINDING AND LAPPING
GRINDING WHEELS AND GRINDING
The Commercial Abrasives
Emery, corundum, carborundum, and alundum are the ordinary
commercial abrasive materials. They vary in hardness, though it
does not follow that the hardest grit is the best for cutting purposes;
the shape and form of fracture of the particles must also be taken
into consideration. We may imagine a wheel made up from dia-
monds, the hardest substance in nature, and whose individual ker-
nels were of spherical form; it is quite obvious that it would be of
little service as a cutting agent; on the other hand, if these kernels
were crystalline or conchoidal in form it would probably be the ideal
grinding wheel.
Emery is a form of corundum found Avith a variable percentage of
impurity; it is of a tough consistency and breaks with a conchoidal
fracture.
Corundum is an oxide of alimiinum of a somewhat variable piurity
according to the neighborhood in which it is mined; its fracture is
conchoidal and generally crystalline.
Carborundum is a silicide of carbon and is a product of the electric
furnace; it breaks with a sharp crystalline fracture.
Alundum is an artificial product, being a fused oxide of aluminum.
It is of uniform quahty with about 98 per cent, of purity. It breaks
with a sharp, conchoidal crystalline fracture and has all the tough-
ness of emery.
Grit and Bond
A GRINDING wheel is made up of the "grit" or cutting material,
and the bond. The cutting efhciency of a wheel depends largely on
the grit; the grade of hardness depends principally on the bonding
material used. The efficiency in grinding a given metal is dependent
largely upon the "temper," or resistance to fracture, and, as noted
above, upon the character of fracture of the grit or cutting grains of
the wheel.
The function of the bond is not only to hold the cutting particles
of the wheel together and to give the wheel the proper factor of safety
at the speed it is to be run, but it must also be possible to vary its
tensile strength to fit the work it is called upon to do. We often hear
the operator say that the wheel is too hard or too soft. He means
that the bond retains the cutting teeth so long that they become
dulled, and this wheel is inefficient; or, in the case of a soft wheel,
the bond has not been strong enough to hold the cutting teeth and
they are puUed out of the wheel before they have done the work
expected.
208
GRINDING WHEELS AND GRINDING 209
The bond to be used for a given operation depends on the wheel
and work speeds, area of wheel in contact with the work, vibration in
wheel spindle or work, shape and weight of work, and many other
like variables.
Wheels are bonded by what are known as the vitrified, silicate,
elastic and rubber processes. No one bond makes a superior wheel
for all purposes; each one has its field.
The vitrified bond is made of fused clays, is unchanged by heat
or cold, and can be made in a greater range of hardness than any
other bond. It does not completely fill the voids between the grains,
and, therefore, a wheel bonded in this way having more clearance
than any other, is adaptable for all kinds of grinding except where
the wheel is not thick enough to vvdthstand side pressure. This bond
has no elasticity.
The silicate bond is composed of clays fluxed by silicate of soda at
low temperatures. It is not as stable as the vitrified bond as regards
dampness, gives less clearance between grains, and has a range of
hardness below that of the vitrified in the harder grades. This bond
has no elasticity and will not make a safe wheel of extreme thinness.
The elastic bond is composed of shellac and other gums. It com-
pletely fills the voids of the wheel, has a limited range of grades, has
a high tensile strength and elasticity, and can be used for the making
of very thin wheels. The rubber or vulcanite bond has the general
characteristics of the elastic, but its grades of hardness cannot be
varied to the same extent and its uses are limited.
Grain and Grade
Grinding wheels are made in various combinations of coarseness
and hardness to meet the variety of conditions under which they
are used. The cutting material is crushed and graded from coarse
to fine in many sizes designated by number. Thus the sizes of grain
used in the Norton wheels are numbered 10, 12, 14, 16, 20, 24, 30,
36, 46, 50, 60, 70, 80, 90, 100, 120, 150, 180, 200. Finer grades
known as flour are also used, sometimes these being designated as
F, FF, FFF, etc. By No. 20 grain is meant a size that wiU pass
through a grading sieve having 20 meshes to the hnear inch.
The term "grade" refers to the degree of hardness of the wheel or
the resistance of the cutting particles imder grinding pressure. A
wheel from which the cutting particles are easily broken, causing it
to wear rapidly, is called soft, while one which retains its particles
longer is called hard.
Minimum Thickness of Wheels
Tables 1,2, and 3 by the Norton Company, show minimum thick-
ness of wheels made by the different processes. A wheel of fine grit
can be made thinner than a wheel of coarse grit, and have the same
factor of safety. The minimum thickness depends upon both the
diameter and the coarseness of the grit used.
For example, a 24-inch vitrified wheel of No, 10 or No. 12 grain
should not be made thinner than 2 inches, while if a grain No, 36 or
finer is used it is considered a safe wheel at i inch thick.
2IO
GRINDING AND LAPPING
Table i. — Minimum Thickness of Elastic Wheels
Grain
14 and 16
20 and 24
30 and 36
46 and 60
70 and finer
Diameter in
Inches
Minimum Thickness of Wheels in Inches
28 to 30
f
3
3
f
1
24 to 26
f
8
^
i
i
20 to 22
h
h
t
t
f
16 to 18
t
f
1
4
1
4
1
4
14 to 15
\
i
A
A
A
10 to 12
A
A
1
i
7 to 9
A
i
i
jg
tV
5 to 6
t\
1^
T^.
tV
A
3 to 4
T%
i
A
3V
3V
I to 2
t\
'
A
3V
^\
Table 2. — Minimum Thickness of Vitrified Wheels
Grain
10 and 12
14 and 16
20 and 24
30
36
46
50 to 120
ISO and finer
Diameter
in Inches
M
mimum Thickness of Wheel i
n Inches
32 to 36
2h
2h
2
2
2
2
2
2
24 to 30
2
2 ,
li
li
I
I
I
I
20 to 22
ih
ih
ll
i\
I
3
4
1
3
16 to 18
Ih
li
I
I
3
3
J
1
14 to 15
li
li
f
3
4
f
h
1
f
10 to 12
li
li
1
^
i
8
f
i
7 tog
I
I
3
4
fV
i
I
S to 6
I
I
3
4
1
i
-
T%
3 to 4
I
i
1
i
t\
i
i
I to 2
3
4
1
4
i
i
i
Smaller
than I In.
tV
tV
GRINDING WHEELS AND GRINDING
211
Table 3. — Minimum Thickness of Silicate Wheels
Grain
10, 12, 14,
and 16
20 and 24
36
40 and so
60 to
120
Wire Web
With
With-
out
With
With-
out
With
With-
With
With-
out
With
With-
out
150
and
finer
Without
Diameter
in Inches
Minimum Thickness of WT^eel in Inches
44 to 48
38 to 42
32 to 36
28 to 30
24 to 26
20 to 22
16 to 18
14 to 15
10 to 12
7 tog
5 to 6
3 to 4
I to 2
3
2
3
2
3
2
3
2
2t
2
2h
2
25
2
2h
2
2\
li
2\
I§
2i
I^
I^
2
2
2
2
I
2
l|
2
I
2
I
2
I^
A
I
Ij
I
I-i
I
I
3
I
f
I
1
I
I
I
\
I
1
3
\
\
1
1
f
\
\
1
i
3
f
Grading of Wheels
Or the many firms engaged in the manufacture of grinding wheels
there are probably no two which have a similar method of grading
or designating the hardness of their wheeels. The Norton Company,
which is probably the oldest in the field, uses the letter method, which
may be said to be the simplest. That is, they take M for their me-
dium-hard wheel and the letters before M denote in regular alphabet-
ical progression the progressively softer wheels. ISIoreover they use
a -\- mark for denoting wheels which vary in temper from the stand-
ards. Thus a wheel may be harder than the standard K, and still
be not so hard as the standard L; in this case it is known as K -f.
The Carborundum Company adopts a somewhat similar method
of grading, the difference being that although M denotes its medium-
hard wheel the letters before M denote the progressively harder
grades. Various other American companies use the letter method
of grading to some extent, but all have individual ideas as to v/hat
degree of hardness should constitute an M or medium-grade wheel.
Then there are firms both in America and on the continent of Europe
which discard the letter method of grading or else use it in conjunc-
tion with numbers or fractions of numbers such as 2H, i|M and
so on.
212 GRINDING AND LAPPING
The selection of suitable wheels for machine grinding may be said
to be governed by the following points, namely, the texture of the
material to be ground, the arc of wheel contact with work and the
quality of finish required. The first and last of these points can for
convenience' sake be taken in conjunction. The quality of surface
finish is dependent on the condition of the wheel face and depth of
cut rather than on the fineness of the grit in the wheel. A wheel
of so fine a grit as loo will give an indifferent finish if it is not turned
true and smooth.
It may be assumed that for all general purposes the aim in view
is to procure a wheel which will fulfil tv/o conditions, that is, that it
shall first remove stock rapidly and at the same time give a decent
finish. Wheels made from a combination of grit of different sizes
are the best for this purpose, as may be seen from the following
explanation. Coarse wheels of an even number of grit will remiove
stock faster than will fine wheels of an even number, because their
depth of cut or penetration is greater. They, however, fail in giving
a high surface finish except in grinding very hard material, because
they are not compact enough.
The Combination Grit Wheel
With the combination wheel the conditions are different and it
seems better at removing stock than does the coarse, even grit wheel.
It may be safe to assume from this that something of a grindstone
action takes place, that is, that the finer particles of grit become
detached from the bond and both roll and cut in their imprisoned
condition between the larger particles. For finishing purposes this
wheel has all the compactness and smooth face of a wheel which
was made solely from its finest number of grit; and for roughing,
it enables a depth of cut to be got which is within the capacity of
its largest kernels.
With regard to the texture or hardness of material ground it may
be taken as a general rule that the harder the material is, the softer
the bond of wheel should be, and that cast iron and hardened steel
bear some relation to each other as far as grinding wheels are con-
cerned, for the same wheel is usually suitable for both materials.
Too large an assortment of wheels is likely to lead to confusion
and we may take the Norton plain cylindrical grinding machine as
being a case in point of a limited assortment of wheels; at the same
time it will be a starting point to illustrate choice of wheels under
various grinding conditions. In this machine four different grade
wheels, all of 24 combination grit, are found sufficient for all classes
of material that it is ordinarily required to grind. These include
high- and low-carbon steels, cast iron, chilled iron, and bronze or
composition metals. These wheels are graded J, K, L, and M.
Hard Wheels
One of the greatest advantages accruing from grinding is that it
ignores the non-homogeneity of material and that it machines work
with the lightest known method of tool pressure, thus avoiding all
deflections and distortions of material which are a natural result of
GRINDING WHEELS AND GRINDING 213
the more severe machining processes. Yet these objects are too
often defeated by the desire for hard and long-lived wheels. A wheel
that is too hard or whose bond will not crumble sufficiently under
the pressure of cut will displace the work and give rise to many
unforeseen troubles. It is also a prolific cause of vibration which
is antagonistic to good and accurate work. The advanta.ge claimed
for it, that it gives a better surface finish, is a deceptive one, for it
mostly obtains this finish at the expense of accuracy. Quality of
finish, that is, accurate finish, is merely a question of arranging of
work speed, condition of wheel face and depth of cut. In the ma-
chine mentioned the suitability of wheels to materials and conditions
is found to be as follows, the wheels being in each case of a combi-
nation of alundum grit:
For hard chilled iron and large diameters of cast iron and
hardened steel , 24 J
For medium chilled iron and medium diameters of cast iron
and hardened steel and bronze 24 K
For all grades of steel which are not hardened and for bronze 24 L
For very low carbon machine steels 24 M
The table given may, speaking generally, be what would be chosen
in the way of wheels for the materials given, and in actual practice
they soon give evidence as to whether they are suitable. It may be
gathered from the table that diameter of work is a factor in the choice
of a wheel. This refers to area of wheel contact and is governed
by what is shown in the table when broad differences of diameter
occur; for instance, it might be necessary to use the K wheel for a
large diameter of high carbon steel if the L wheel was evidently too
hard.
Speed and Efficient Cutting
The efficient cutting of a wheel depends very much on the speed
of the work, and an absence of knowledge in this respect may often
lead to a suitable wheel's rejection. Revolving the wheel at the
speed recommended by the maker is the first necessity, and if it is
found unsuitable after experimenting with various speeds it should
be changed for a softer or harder one as the conditions indicate.
Starting from the point that a wheel is desired that shall remove
the maximum amount of stock with the minimum amount of wear
on the wheel, the indications and method of procedure may be as
follows; only it must be understood that this refers to cases where
an ample supply of water is being delivered at the grinding point.
If, after trying all reasonable work speeds, a wheel should burn the
work, or refuse to cut without excessive pressure, or persistently
glaze the surface of the work, it is too hard for that particular work
and material and may be safely rejected. If, after trying all reason-
ably reduced work speeds, a wheel should lose its size quickly and
show all signs of rapid wear, it is too soft for that particular work and
material and may be rejected. These indications refer to all ordi-
nary cases and it may be gathered that the most economical wheel
is that which acts in such a manner as to be a medium between the
two cases. There is still another point to bear in mind with regard
to the size of the grit in the wheel, but which refers more especially
214
GRINDING AND LAPPING
to very hard materials such as chilled iron. Either a coarse or com-
bination wheel may go on cutting efficiently in roughing cuts because
pressure is exerted, but may begin to glaze when this pressure is
•much relieved as in finishing cuts. A careful microscopic scrutiny
of a wheel that displays this tendency would seem to lead to the fol-
lowing assumption:
When a Wheel is Sharp
The wheel face when newly trued with the diamond tool, which
is necessary to obtain an accurate finish, shows a promiscuous ar-
rangement of particles, some of which present points and others
present a broader face with a rough and granular surface. When
the wheel is presented to the hard surface of the work the high points
of this granular face and the sharp contour of the kernels will go on
cutting until they are dulled and worn down, after which their face
FIG. 1
Grinding
Small Dia.
FIG. 2 FIG. 3
Gdnding Large Dia. Grinding
Flat S.urface.
Contact of Wheel
FIG. 4
Internal Grindi
area is too great to enter the surface without undue pressure. When
the wheel has reached this condition the microscope shows these
broader-faced kernels polished to a metallic luster, which bears out
the explanation tendered and also makes the remedy quite appar-
ent. This is to use a wheel of very fine grit for finishing purposes
in these cases or else keep the coarser wheel in condition by repeated
dressings with the diamond tool.
Wheel Contact
Reference to Figs, i to 4 will show what actual practice requires
'in the choice of a wheel so far as the question of wheel contact is
concerned. A wheel is shown in contact with four different vari-
eties of work, all of which we will suppose to be of the same mate-
rial, the depth of cut, much exaggerated, being the same in each case.
In the first case it is a shaft of small diameter, and the wheel contact
being the smallest the harder grade of wheel would be suitable, com-
paratively speaking. Assuming that this wheel was found to be
suitable it would probably require a softer wheel for the next case,
which is a shaft of larger diameter, and the wheel contact propor-
tionately greater. To continue the comparison still further, the third
GRINDING WHEELS AND GRINDING 215
case shows the wheel engaged in grinding a flat surface, and the
fourth is a wheel grinding internally. In each case practice demands
that the wheel shall be progressively softer in bond or grade and is
some proof of a consistency in the action of grinding wheels.
The Contact Area of a Wheel
The most probable explanation of this may be that as the contact
area increases more work is required from each individual kernel of
grit and it the sooner becomes dulled; this requires that the bond
must be more friable both to allow it to escape easily and to minimize
the pressure required to make the wheel cut as the cutting area
becomes greater. Following on this reasoning we are able to choose
a list of wheels which would be suitable for almost all purposes, and
which would be as follows if of Norton grade:
For plain cylindrical grinding
J K L M
For grinding plane surfaces
H I J K
For internal grinding
F H I J
This collection of wheels would be suitable for almost any type
of grinding machines, though when the wheels are exceptionally nar-
row a grade or one-half grade higher might be possible; it would,
of course, be a matter for a little trial and experiment. The wheels
for external cylindrical work may preferably be combination wheels,
but for plane surface and internal work they are better made of
single grit, about 36 or 46. The great contact area of wheel in these
two classes of work is liable to generate much heat so that an open
and porous wheel is preferable.
Wheel Pressure and Wear
As the wheel is a disk built up from a numerous assortment of
minute cutting tools which are held in position by a more or less
friable bond, in using it we must bring it to bear on the work with
a pressure that shall not be so great as to tear these minute tools
from their .setting until their cutting efficiency is exhausted, for if we
do so we are wasting the wheel. To gage the exact amount of the
pressure required is a matter of judgment and experience, though
where automatic feeds are provided on a machine the right amount
of pressure or feed is soon determined. It will also be readily under-
stood that a regular automatic feed is more reliable for the purpose
than a possibly erratic hand one. The automatic feed may be set
to give a certain depth of cut at each pass of the wheel, and its amount
of wear noted; if this wear be found excessive the depth of cut may
be reduced. It must not be here forgotten that work speed also
enters into this consideration and that a high work speed will tend
to wear the wheel excessively; inversely a reduced work speed will
reduce the amount of wear. Having these points in mind the right
combination of depth of cut and work speed is soon arrived at, and
an approximate judgment attained for the future.
2i6 GRINDING AND LAPPING
Grinding Allowances
The amount of stock left for removal by the grinding wheel and
the method of preparing the work have both much bearing on the
economic use of grinding wheels, and heavy and unnoticed losses
often occur through want of a few precautionary measures. The
necessary amount of stock to leave on a piece of work as a grinding
allowance depends firstly on the type of machine employed, the class
of labor engaged in preparing it, and whether it has to be hardened
or otherwise.
In powerful machines, which will remove stock rapidly, the grind-
ing allowance may be anything up to 3^2 inch. There are many
cases of an especial character when the grinding allowance stated
may be exceeded to advantage so long as discretion is used. Straight
shafts may often be ground direct from the black bar of raw material
■jV inch above finished size, or when shafts of this character must
have large reduction on the ends they can be roughly reduced in the
turret lathe while in their black state and finished outright more
economically in the grinding machine. Very hard qualities of steels
or chilled rolls are other cases where it is often more economical to
use the grinding machine without any previous- machining process,
and though there may be sometimes an alarming waste of abrasive
material its cost is as nothing compared with other savings that are
made.
Grinding allowances for hardened work are usually larger than
for soft work, to allow for possible distortion; so that individual
experience alone can determine the amount to be left. It is suffi-
cient to say that the allowances on case-hardened or carbonized work
should not be excessive; otherwise the hardened surface may be
ground away.
Grinding Hardened Work
As far as the actual grinding of hardened work goes, it is indis-
pensable that the whole portion of a piece that is to be ground should
be roughed over previous to the final finishing; if it is at all possible
to allow some little time to elapse between the two operations so
much the better, more especially if it has bent in hardening and been
afterward straightened; this will allow of the development of any
strain that may be present. Both for special and standard work in
a factory a table of grinding allowances can be compiled as a result
of experience and posted in a conspicuous position. If this be done
and trouble taken to see that it is adhered to, it will save much trouble
and be a means of avoiding much unnecessary expense.
It is necessary to slightly undercut the corners of shoulders so
as to preserve the corner of the grinder's wheel intact. A piece of
work should never be prepared in such a manner as to form a radius
on the corner of the wheel, for to get the wheel face flat again means
much waste of wheel and wear of diamond. Where fillets or radii
are necessary they are better got out with a tool, for even if they
are to be ground they must be turned good to allow the wheel to
conform to their shape. The only excusable reason for grinding a
round corner is when the work is hardened or in some special case
where the expense incurred is warranted.
GRINDING WHEELS AND GRINDING
217
GRINDING ALLOWANCES FOR VARIOUS LENGTHS
AND DIAMETERS
Table 4 shows the practice of the Landis Tool Company, in refer-
ence to grinding allowances. This table covers work up to 12 inches
diameter, and lengths to 48 inches.
Table 4. — Allowances for Grinding
(Landis Tool Co.)
Length
3"
6"
9"
12"
15"
18"
24"
30"
36"
42"
48"
Diam.
j .010
.OIO
.010
.010
.015
.015
.015
.020
.020
.020
.020
3
.0x0
.010
.010
.010
.015
015
.015
.020
.020
.020
.020
I
.010
.010
.010
■OIS
.015
.015
.015
.020
.020
.020
.020
^i
.CIO
.010
•OIS
.015
.015
•OIS
•OIS
.020
.020
.020
.020
li
.010
.015
•015
•OIS
.015
•OIS
.020
.020
.020
.020
.020
2
•ois
.015
.015
.015
.015
.020
.020
.020
.020
.020
.025
2\ '
.015
.015
.015
.015
.020
.020
.020
.020
.020
.025
.025
2i
.015
.015
.015
.020
.020
.020
.020
.020
.025
.025
.025
3
.015
.015
.020
.020
.020
.020
.020
.025
.025
.025
.o„
3§
.015
.020
.020
.020
.020
.020
.025
.025
.025
.025
.025
4
.020
.020
.020
.020
.020
.025
.025
.025
.025
.025
.030
4i i
.020
.020
.020
.020
.025
.025
.025
•025
.025
.030
.030
5
.020
.020
.020
.025
.025
.025
.025
.025
.030
.030
.030
6 i
.020
.020 1
.025
.025
.025
.025
.025
.030
.030
.030
.030
7 1
.020
':::r'
•025
.02s
.025
-025
.030
.030
.030
.030
.030
' i
.025
.025
.025
.025
.025
.030
.030
.030
.030
.030
.030 •
9
.025
.025
.025
.025
.030
.030
.030
.030
.030
.030
.030
10 1
.025
.025
.025
.030
.030
.030
.030
.030
.030
.030
.030
II 1
•025
.030
.025
.030
.030
.030
.030
.030
.030
.030
.030
.030
12
■030
.030
.030
.030
.030
.030
.030
.030
.030
.030
2l8
GRINDING AND LAPPING
OTHER GRINDING ALLOWANCES
Table 5 gives the allowances of the Brown & Sharpe Mfg. Co. in
rough turning work for the grinding department. Limit gages of the
form sho^vn are used, 4:he dimensions in the table covering work up
to 2 inches diameter.
Table 5. — Limit Gage Sizes for Lathe
Work which is to be Finished
BY Grinding
(Brown & Sharpe Mfg. Co.)
Size
Not go on
Go on
•
Size
Not go on
Go on
Size
Not go on
Go on
Inches
Inches
Inches
.
0.383
0.387
U
0.94SS
0.9495
If
1.508
1.512
I6
0.4455
0.4495
I
008
1.012
ire-
1.5705
1.574s
0.508
0.512
irV
0705
1.0745
It
1-633
1.637
I6
0.5705
O.S745
li
133
1. 137
lu
1.695s
1.6995
0.633
0.637
Il^6
1955
I.I995
ri
1.758
1.762
ii
0.6955
0.6995
li
258
1.262
m
1.820S
1.8245
f
0.758
0.762
Il\
3205
1.3245
i^
1.883
1.8875
H
0.8205
0.824s
I*
383
1.387
rik
1.9455
1.949
i
0.883
0.887
Il'e-
1-4455
1-4495
2
2.008
2.0I2
Use of Water
Water should be applied at the right spot. This spot must be
right at the grinding point, whether it be internal, external, or plane-
surface work, and must be delivered ^vith sufficient force to keep
the wheel face clean. If this is not done there is a kind of mud
accumulated at the grinding point, which causes glazing. Water is,
or should be, used in grinding process not as a means of quenching
heat but rather to prevent its creation and radiation, and so the
actual grinding point is the best place to apply it.
It is a necessary means of keeping the work at an equable tem-
perature so as to obviate distortion and to make the matter of tak-
ing dimensions an actuality rather than a guessing matter. This
applies equally to all kinds of grinding.
The Use of Diamonds
Here it is perhaps weU to give the question of diamonds some little
consideration as they are sometimes a very expensive item. A dia-
mond is a very essential part of a grinding machine's equipment, for
in its absence a good and higlily finished grade of work is an impos-
sibility. It is perhaps unnecessary to state that they should be the
hardest rough stones procurable, and that the larger they are the
cheaper they are in the end. With regard to their size: This is a
GRINDING WHEELS AND GRINDING
219
known proportionate element in their price per carat, but a large
stone allows of a more secure hold in its setting and so the danger
of losing it is reduced. As a further precaution against this danger
the diamond tool should always be held by mechanical means when
using it except in cases- which are unavoidable; this may be in cases
where profile shapes have to be turned on the wheel face. An
attempt to turn by hand a perfectly flat face on a wheel, which is
necessary for finishing, must of a necessity end in failure.
As a means of preservation of the diamond a full stream of water
should be run on it when in use and many hght chips are preferable
to' a few heavy ones. The m.ain thing is to watch that it does not
get unduly heated, for this is disastrous to it. Where large quanti-
ties of material have to be removed from a wheel the ordinary wheel
dresser may be employed to reduce the bulk of the stock, and the
diamond only used for finishing to shape.
Setting the Diamonds
Diamonds may be obtained ready fixed in suitable holders or the
rough stones maj^ be bought and set by any competent toolmaker.
The illustrations show various methods by which they may be held
securely and require but httle explanation. First, Fig. 5 is the
method most commonly used, the diamond being either peened or
brazed in position. One disadvantage of this method is that the
diamond is apt to break with a chance blow of the peening chisel,
or the heat from brazing will sometimes cause fractures; neither is
it so easily reset when its point becom.es dulled as are the other
methods shown. Fig. 6 requires no explanation except that it is
advisable to pack the diamond with shredded asbestos fiber to act
as a cushion; this method allows of quick resetting. Fig. 7 consists
H._.-J
riG. 5
FIG. 6 FIG. 7
Methods of Setting Diamonds
FIG. 8
of a small steel cap tapped out to fit the stock as shown. Enough
shredded asbestos fiber is inserted between the diamond and stock
to hold it firmly in position. This method also allows of quick and
safe resetting. The fourth method. Fig. 8, is covered by patent
rights and its advantage can be seen at a glance; as the diamond
wears, the small peg containing it can be revolved in the stock to
present a new cutting edge and be so clamped in position.
220
GRINDING AND LAPPING
Speed Tables, Rules for Surface Speeds, etc.
The table below gives the number of revolutions per minute at
which grinding wheels of diameters ranging from i to 60 inches must
be operated to secure peripheral velocities of 4000, 5000, 5500 and
6000 feet per minute. Ordinarily a speed of 5000 feet per minute
is employed, though sometimes the speed is somewhat lower or
higher for certain cases.
Grinding Wheel Speeds
Rev. per Minute! Rev. per Minute Rev. per Minute
Rev. per Minute
Diameter
Wheel
for Surface Speed for Surface Speed 1 for Surface Speed
for Surface Speed
of 4000 ft.
of 5000 ft.
of 5500 ft.
of 6000 ft.
I Inch
15,279
19,099
21,000
22,918
2 Inches
7,639
9,549
10,500
11,459
3 Inches
5,093
6,366
7,350
7,639
4 Inches
3,820
4,775
5,250
5,730
5 Inches
3,056
3,820
4,200
4,584
6 Inches
2,546
3,183
3,500
3,820
7 Inches
2,183
2,728
3,000
3,274
8 Inches
1,910
2,387
2,600
2,865
10 Inches
1,528
1,910
2,100
2,292
12 Inches
1,273
1,592
1,750
1,910
14 Inches
1,091
1,364
1,500
1,637
16 Inches
955
1,194
1,300
1,432
18 Inches
849
1,061
1,150
1,273
20 Inches
764
955
1,050
1,146
22 Inches
694
868
950
1,042
24 Inches
637
976
875
955
26 Inches
586
733
800
879
28 Inches
546
683
750
819
30 Inches
509
637
700
764
32 Inches
477
596
650
716
34 Inches
449
561
620
674
36 Inches
424
531
580
637
38 Inches
402
503
550
603
40 Inches
382
478
525
573
42 Inches
364
455
. 500
546
44 Inches
347
434
475
5^J
46 Inches
332
41S
455
498
48 Inches
318
397
440
477
50 Inches
306
383
420
459
52 Inches
294
369
405
441
54 Inches
283
354
390
42s
56 Inches
273
341
375
410
58 Inches
264
330
360
396
60 Inches
255
319
350
383
The exact speed at which any specified wheel should be run depends
upon several conditions, such as the t>TDe of machine, character of
work and wheel, quality of finish desired and various other factors
referred to at other places in this book. Wheels are ordinarily run in
practice from about 4090 to 6000 feet per minute, though in some
cases a speed as high as 7500 feet has been employed. An average
GRINDING WHEELS AND GRINDING
221
speed recommended by most wheel makers is 5000 feet. To allow
an ample margin of safety it is recommended that wheel speeds
should not exceed 6000 feet per minute.
The table of circumferences below will be of service in connection
with the finding of surface speeds and spindle revolutions per minute.
Circumferences of Grinding Wheels
Diameter
Circumference
Diameter
Circumference
Diameter
Circumference
of Wheel
of Wheel in
of Wheel
of Wheel in
of Wheel
of Wheel in
in Inches
Feet
in Inches
Feet
in Inches
Feet
I
.262
25
6.546
49
12.838
2
•524
26
6.807
50
13.090
3
.785
27
7.069
51
13.352
4
1.047
28
7.330
52
13.613
5
1.309
29
7.592
53
13.875
6
1. 571
30
7.854
54
14.137
7
1.833
31
8.116
55
14.499
8
2.094
32
8.377
56
14.661
9
2.356
33
8.639
57
14.923
10
2.618
34
8.901
58
15.184
II
2.880
35
9.163
59
15.446
12
3.142
36
9.425
60
15.708
13
3.403
37
9.687
61
15.970
14
3.665
38
9.948
62
16.232
15
3.927
39
10.210
63
16.493
16
4.189
40
10.472
64
16.755
17 ,
4.451
41
10.734
6S
17.017
18
4.712
42
10.996
66
17.279
19
4.974
43
11.257
67
17.541
20
5. 236
44
II. 519
68
17.802
21
5.498
45
II. 781
69
18.064
22
5.760
46
12.043
70
18.326
23
6.021
47
12.305
71
18.588
24
6.283
48
12.566
72
18.850
Thus, to find the surface speed of a wheel in feet per minute :
Rule. — Multiply the circumference as obtained from the table,
by the number of revolutions per minute.
Example. — A wheel 18 inches diameter makes 1060 revolutions
per minute. What is the surface speed, in feet, per minute?
4.712 X 1060 = 5000 feet surface speed.
When the surface speed and wheel diameter are given, to find the
number of revolutions of the wheel spindle :
Rule. — Divide the surface speed in feet per minute by the cir-
cumference.
Example. — A wheel 24 inches diameter is to be run at 6000 feet
surface speed per minute. How many revolutions shoidd the wheel
make?
6000 ^ 6.283 = 962, number of revolutions per minute the wheel
should make.
222 GRINDING AND LAPPING
GRADING ABRASIVE WHEELS
The Norton Company uses 26 grade marks, the Carborundum
Company 19, while the Safety Emery Wheel Company uses 40. The
following table is a comparison between the grade designations of the
Norton Company and the Carborundum Company. Intermediate
letters between the grade designations indicate relative degrees of
hardness between them; the Norton Company manufacturing four
degrees of each designation, while the Carborundum Company man-
ufactures three.
Norton Co.
Grade Designation
Carborundum
Co.
A
"b.
H
Extremely or
Very Soft
Soft
Medium Soft
Medium
Medium Hard
Hard
Extremely or
Very Hard
Y
. U
Q
C.
G
T
R
D.
F.
s
E
T
p
J
P
0
•
K
K
0
N
L
T,
N .
M ...
M
Q
J
R
X
I
E
S
w
H
F
T .
y
G
U ....
Y
D
Z
The Safety Emery Wheel Company's grade list is an arbitrary one
with the following designations:
C. Extra Soft
A. Soft
P. Medium
O. Hard
E. Extra Hard
H. Very Soft
M. Medium Soft
I. Medium Hard
N. Very Hard
D. Special Extra Hard
GRINDING WHEELS AND GRINDING
223
Intermediate figures between those designated as soft, medium
soft, etc., indicate so many degrees harder or softer, e.g., K\ is one
degree harder than soft. Af is three degrees harder than soft or
one degree softer than medium soft.
Numbers and Grades of Abrasive Wheels
In the following table for the selection of grades will be found a
comparison of the grading used by the Norton Company, and that
of the Carborundum Company:
Class of Work
Large Cast Iron and Steel Castings
Small Cast Iron and Steel Castings
Large Malleable Iron Castings . .
Small Malleable Iron Castings . .
Chilled Iron Castings
Wrought Iron
Brass Castings
Bronze Castings
Rough Work in General
General Machine Shop Use
Lathe and Planer Tools
Small Tools
Wood- working Tools
Twist Drills (Hand Grinding) . . .
Twist Drills (Special Machines) .
Reamers, Taps, Milling Cutters,
etc. (Hand Grind)
Reamers, Taps, Milling Cutters,
etc. (Spec. Mach.)
Edging and Jointing Agricultural
Implements
Grinding Plow Points
Surfacing Plow Bodies
Stove Mounting
Finishing Edges of Stoves
Drop Forgings
Gumming and Sharpening Saws .
Planing Mill and Paper Cutting
Knives
Car Wheel Grinding
Norton Co.
Number
Usually
Furnished
16 to
20 to
16 to
20 to
16 to
16 to
16 to
r6to
16 to
30 to
30 to
36 to
36 to
36 to
46 to
46 to :
46 to
16 to
i6to
20 to
20 to
30 to
20 to
36 to
30 to
20 to
30
20
30
20
30
30
30
30
46
46
100
60
60
60
Grade
Usually
Fvumished
QtoR
PtoQ
QtoR
PtoQ
QtoR
PtoQ
OtoP
PtoQ
PtoQ
OtoP
NtoO
NtoP
MtoN
MtoN
KtoM
NtoP
HtoK
QtoR
PtoQ
NtoO
PtoQ
OtoP
PtoQ
MtoN
JtoK
OtoP
Carborundum Co.
Number
Usually
Furnished
16 to 24
20 to 30
16 to 24
20 to 30
16 to 24
16 to 24
20 to 36
20 to 30
20 to 30
24 to 36
30 to 36
50 to 80
40 to 60
60
50
50 to 80
50 to 60
141 to 24
20 to 24
16 to 20
24 to 30
24 to 30
241036
403-603
202 — 60
to 80
16 to 24
Grade
Usually
Furnished
GtoH
GtoH
GtoH
Htol
H
FtoH
Htol
I
H
Gto J
I to J
I to J
LtoM
I to J
LtoO
KtoN
LtoM
Gto I
H
G
G
G
Gtol
JtoL
MtoR
H
224
GRINDING AND LAPPING
THE SHAPES OF WHEELS
Although grinding wheels are manufactured in a great variety of
shapes and sizes, there are a few general forms into which they may
be grouped. Practically'' all of the hundreds of commonly used shapes
made for the various tj'pes of grinding machines and for the different
kinds of work come under some one of these classifications, the
most common of which may be designated as "disk," "cup," "cylin-
Cylinder
Fig. 9. — Shapes of Wheels
-9H—
Cup
THE SHAPES OF WHEELS
225
der " and " saucer " wheels. These shapes and some of their modifica-
tions are included in the groups of wheels illustrated in Figs. 9-10.
These wheels are in most cases made in numerous widths and
diameters, and the dimensions given in any such instances merely
Pot Balls
Fig. 10 — Shapes of Wheels
show the proportions of one size of wheel selected as t3'pical from
the comprehensive Hsts of wheel manufacturers' products.
Of the wheels shown, A and B are plain disks; C is an offset disk
used on cylindrical grinders for grinding close up to a gear, collar, or
piston head of large radius; D is a disk wheel for different makes of
226 GRINDING AND LAPPING .
tool and roll grinders, E, EE, F, G and H are "ring" wheels which are
modifications of the disk t3'pe. The two wheels E and EE are made
on large iron centers and are for use on the Sellers tool grinders. The
other ring wheels referred to are adapted for mounting on large iron
centers, and all such wheels are for service on machines where only
a limited reduction of wheel diameter is permissible.
The shallow cup wheel / is for drill grinders and the larger, deeper
cup wheel / is of a t\^e used extensively on knife-grinding machinery.
.Wheels of this shape and of suitable dimensions, are also used on roll
and cylindrical grinders, and in the smaller sizes on cutters and
reamer grinders.
The wheel K is a plain cylinder for grinding on the end the same
as the cup wheels. Such cylinders are used in various proportions on
vertical surface grinders, edge grinders, etc. They are held in ring
chucks.
Cup and cylinder wheels are coming more and more into use and
are already made in a great variety of diameters and widths. On
certain classes of grinding operations they have marked advantages
over the regular form of wheel as the same diameter is always main-
tained, thus avoiding the necessity of a change in speed, and the
grinding is accomphshed on a flat surface instead of one that is
curved.
The cup wheel L is for the Pratt & Whitney vertical surface grinder.
The small wheels in group M are for internal grinding operations
in holes of limited diameter. The larger internal wheel R is for the
Heald cylinder grinder. Three forms of the "saucer" wheel for cutter
grinders are illustrated at N, 0 and P, and two bevel-edge cup wheels
are showTi at S, and T, both being made for cutter grinder use. The
double-edge cup wheel can be used for sharpening both sides of a
straddle mill without reversing the latter on its arbor; it is also useful
in such operations as grinding out parallel surfaces, say the jaws of a
snap gage. '
The conical wheel at Q is for a tool grinder and is used principally
for sharpening pattern makers' gouges which are beveled on the inside
of the curve.
Two saw gummers, representative of a number of shapes regularly
made, are shown at U. These are adapted for sharpening saw teeth
and grinding dowTi in the "gullet" or concave space between the
bottoms of the teeth.
The "pot balls" at N and IF are used in grinding out hollow ware
such as pots and kettles. These are made in great variety to suit
spherical receptacles, skillets, flat bottom pots, etc.
MOUNTING GRINDING WHEELS
One of the most important considerations in connection with the
use of grinding wheels is that they shall be properly mounted, upon
suitably proportioned spindles and between properly designed flanges.
A wheel which is crowded upon a spindle of weak design, or which is
cramped between two imperfect flanges that are either too small or
take a bearing upon the wheel at the wrong point, is subjected to condi-
tions as likely to cause an accident as is an excessive rate of speed.
MOUNTING WHEELS
227
The vast number of abrasive wheels in use upon the class of ma-
chines commonly known as bench and floor grinders, grinding wheel
stands, emery grinders, etc., and which are so generally in service at
various points about the machine shop, blacksmith shop and foundry,
makes it desirable that something should be said here in reference to
the best methods of mounting wheels on such apparatus.
In the first place, the machine itself should be of rigid construc-
tion, with spindle of ample proportions; the bearings should be well
fitted; and kept well oiled so that the arbor will not become over-
heated and by expanding, break the wheel; and the machine should
be securely fastened on substantial foundations not only to insure
safety but in order to secure better results with the wheel.
The following sizes of spindles are recommended by the Norton
Company and by some other wheelmakers, except where the grinding
wheels are extra thick:
Wheel Spindle
6 in. diameter and less i in.
8 in. diameter and less f in.
10 in. diameter and less f in,
1 2 in. diameter and less i in.
14 in. diameter and less I4 P-
16 in. diameter and less i| in.
18 to 20 in. diameter if in.
22 to 24 in. diameter 2 in.
Larger than 24 in 2I to 3 in.
Fig. II
A B
Right and wrong way to mount v/heels
The flanges should be reheved as at A in Fig. 11, and they should
be at least one-half the diameter of the wheel and have a true bear-
ing at the outer edge. The inner flange should never be loose but in
all cases should be fixed on the spindle. Under no circumstances
should the flanges be allowed to be less than one- third the diameter
228 GRINDING AND LAPPING
of the wheel. Wheels must not be allowed to run when held only
by a nut in place of a flange, as the nut is liable to crawl and cause
accident.
Compressible washers of pulp or rubber, slightly larger than the
flanges, should be used between the flanges and the wheel as shown
at A, Fig. II. These distribute the pressure evenly when the flanges
are tightened, b}^ taking up any imperfections in the wheel or flanges.
The hole in the wheel bushing should be 0.005 ii^ch larger than
standard size spindles. This permits the wheel to sUde on the spindle
without cramping and insures a good fit not only on the spindle
but against the inside flange, which is essential.
The flanges should be tightened only enough to hold the wheel
firmly, thus avoiding unnecessary strain.
General Suggestions
Handle aU wheels with the greatest care in unpacking, storing,
delivering, etc. Wheels are frequently cracked by rough usage before
they are ever placed on the grinding machine. The man in charge
of the storeroom should inspect each wheel before giving it out to the
workman.
Wheels should be stored in a dry place.
A wheel used in wet grinding should not be left overnight partly
immersed in water.
When mounting wheels do not screw up the nut too tight; it
should be set up only enough so that the flanges hold the wheel
firmly.
Keep all rests adjusted close to the wheel so that work camiot be
caught.
Avoid heavy pressm-e of the work on the wheel when grinding.
Keep the wheel true by dressing frequently.
If a wheel vibrates, there is something ^vrong. It should be trued
up and the boxes should be rebabbitted after the journals are
trued up. «
Never hack a wheel; it is unnecessary and dangerous.
Use wheel guards wherever possible.
MAGNETIC CHUCKS
Magnetic chucks have come to be a very necessary part of the
equipment of any surface grinding machine, whether plain or rotary.
Before their coming it was customary to bed thin work in wax on the
platen of a grinder in order to finish the flat sides. Other flat work
had to be held in "fingers" on special fixtures, and on account of
their being very thin and easily sprung, it was diflicult to secure
really accurate work.
The magnetic chuck holds the thinnest pieces of -iron or steel firmly,
draws down any shght spring in the work and prevents springing when
strains are released during the grinding operations.
The chuck face is divided into magnet poles, separated by babbit
or other non-magnetic metals, and coils of insulated wire from these
into electromagnets when current is applied. For rotary work, the
POLISHING WHEELS 229
electric current is supplied by brushes running against insulated con-
tract rings on the outside. Current can be supplied from any incan-
descent lamp socket on a direct current circuit.
Alternating current cannot be used.
A No. o chuck ha\ang a face 10 X 14 inches uses about one-half
as much power as a 16 candle-power lamp.
Hints for Using Magnetic Chucks
The chucks should not be taken apart.
Nothing but iron or steel can be held on the chucks.
The holding power depends on the amount of work surface in con-
tact with the chuck.
Work can be held on edge by using adjustable back rest.
Very thin work can be held for grinding on the edges by laying it
against the back rest and backing it up with a parallel strip.
Thin work will not hold as well as thick work.
In packing a num-ber of small pieces on a chuck at one setting, it
is better to separate them a little Avith strips of non-magnetic material.
Do not plug up the vent holes in the chuck.
Keep water away from the switch, the brushes and the interior of
the chuck.
Magnetic chucks do not take the place of all other chucks.
Do not use water on chucks except where they are made for it.
Chucks are usually wound for no or 220 volts for direct current
only.
POLISHING WHEELS
There are many varieties of polishing wheels in use, the principal
kinds being kno\\Ti as wooden wheels, compressed wheels, canvas and
mushn, seahorse and felt wheels. For good work, and economy in
abrasive, glue and labor cost, wheels and methods must be selected
to suit the work.
A few years ago, the wooden wheel covered with leather and turned
to fit the piece to be polished, was universally used. At the present
time, the wooden, leather-covered wheel is used largely on fiat sur-
faces and on work where it is necessary to maintain good edges.
When this kind of a wheel is made with a double coating of leather,
it makes a first-class finishing wheel.
Compressed wheels, or wheels having a steel center are made \vith
surfaces of leather, canvas or linen. JMany tool shops are equipped
with these wheels exclusively. They answer all piurposes and are
safer and more economical than wooden wheels.
They are also used largely on cutlery and for pohshing chilled plows.
The compressed wheel is of strong construction, is very durable and
easily kept in balance.
Canvas and musUn wheels are used extensively for polishing stoves,
shovels, plows, brass, cast iron and steel. For roughing out and dry
fining on irregular pieces, they have proved very satisfactory. They
hold the abrasive well and require no washing off as they can be
cleaned with a buff stick or an abrasive brick.
230 GRINDING AND LAPPING
Many concerns, such as plow-, shovel- and hoemakers, buy the
canvas and muslin and make their own wheels.
Sea-horse wheels are very expensive, most concerns buying the
hides and making their own wheels.
Where a high-grade polish is required, there is probably no wheel
which can compare with the wheel made of sea horse. They are
largely used on guns, pistols and cutlery.
Felt wheels are largely used by stovemakers for finishing surfaces.
Bull neck wheels are also used for this purpose.
The felt wheels are made from white Spanish and Mexican felt
and are extensively used for finishing on certain classes of work.
Care of Polishing Wheels
Polishing wheels should be kept in perfect balance and running
true at all times. A wheel out of balance wastes time, glue and
abrasive, and will not do as good work.
The most efiicient glue and the best abrasive are the cheapest in
the long run.
The glue pots should be kept clean and the glue properly
cooked before using.
It is also important to heat the abrasive before applying.
The wheels should be kept properly cleaned and thoroughly
covered with the abrasive.
The wheels should be selected for the particular work the same
as in grinding and only the wheel best adapted should be used at all
times.
Polishing operations are usually divided into three classes: rough-
ing, dry fining, and finishing or oiling.
The abrasives used for roughing usually run from numbers 20 to
80. For dry fining, from numbers 90 to 120. The numbers used
for finishing run from 150 to XF.
For both roughing out and dry fining, the polishing wheels should
be used dry. For finishing, the wheels are first worn down a little
and then oil, beeswax, tallow and similar substances are used on the
wheel. This, together with the abrasive, brings up a fine finish.
Speed of Buffing Wheels
Wood, leather covered 7,000 ft. per minute
Walrus 8,000 ft. per minute
Rag wheels 7,000 ft. per minute
Hair-brush wheels 12,000 ft. per minute
Ohio grindstone 2,500 ft. per minute
Huron grindstone 3,500 ft. per minute
LAPPING 231
LAPPING
Lapping may be defined as the process of finishing the surface of
a piece of work by means of another piece of material, called a lap,
the surface of which is charged with an abrasive.
Laps are roughly divided into three general classes. First, those
where the form of the lap makes a line contact with the work, and
the work is, if cylindrical, revolved to develop the cylindrical form,
or, if straight, in one direction, is moved back and forth under the
lap. Second, those which are used for straight surfaces with a full
contact on the lap, and third, those which are used for male and
female cylindrical surfaces with a full contact on the lap. In all
cases the material from which the lap is made must be softer than
the work. If this is not so, the abrasive will charge the work and
cut the lap, instead of the lap cutting the work.
The first class is used in the place of emery wheels, either where
the work is too small to use an ordinary wheel or where a form is
to be ground on the work and an emery wheel will not keep its shape.
They are usually made of machinery steel and the abrasive used is
crushed diamond rolled into the surface. In rolling in the diamond
Fig. I. — A Lapping Plate for Flat Work
dust the sharp corners of the particles cause them to bed securely
into the surface of the lap, and if a good quality of diamond is used,
a lap will grind all day without recharging. Oil is used to lubricate
the work and carry away the dust from the grinding. If a diamond
lap is run dry the particles of diamond tear and raise "burs" in the
work, which strip the lap very quickly. The speed should be about
two-thirds that for an emery wheel of the same size; for if it is ex-
cessive, the lap will wear smooth and glaze instead of cutting. This
kind of lap is used mainly in watch and clock shops, and shops mak-
ing watch tools, sub-press dies, and similar work.
Lapping Flat Surfaces
In lapping flat surfaces, which are usually on hardened steel, a
cast-iron plate is used as a lap and emery as an abrasive. In order
that the plate may stay reasonably straight, it should either be quite
thick, or else ribbed sufficiently to make it rigid, and in any case it
should be supported on three feet, the same as a surface place. For
232 GRINDING AND LAPPING
rough work or "blocking down," as it is called, the lap works better
if scored with narrow grooves, about J inch apart, both lengthways
and crossways, thus dividing the plate into small squares, as in Fig. i.
The emery is sprinkled loosely on the block, wet with lard oil
and the work rubbed on it; care is taken to press hardest on the high-
est spots. The emery and oil get in the grooves, and are continually
rolhng in and out, getting between the plate and the work and are
crushed into the cast iron, thus charging it thoroughly in a short
time. About No. loo or No. 120 emery is best for this purpose.
After blocking down, or if the work has first been ground on a
surface grinder, the process is different. A plain plate is used
with the best quality of flour of emery as an abrasive, as the least
lump or coarseness will scratch the work so that it will be very hard
to get the scratches out. Instead of oil benzine is used as a lubri-
cant and the lap should be cleaned off and fresh benzine and emery
apphed as often as it becomes sticky. The work should be tried
from time to time with a straight-edge and care taken not to let the
emery run in and out from under the work, as this will cause the edges
to abrade more than the center, and will especially mar the corners.
After getting a good surface, the plate and work should be cleaned
perfectly dry, and then rubbed. The charging in the plate will
cut just enough to remove whatever emery may have become charged
in the work, will take away the dull surface and leave it as smooth as
glass and as accurate as it is possible to produce.
Laps for Holes
In lapping holes various kinds of laps are used, according to the
accuracy required, and the conditions under which the work is done.
The simplest is a piece of wood turned cylindrical with a longitu-
^a
m
n^:
Fig. 2. — Laps for Holes
dinal groove or split in which the edge of a piece of emery cloth is
inserted. This cloth is wound around the wood until it fills the hole
in the work. This is only fit for smoothing or enlarging rough holes
and usually leaves them more out of round and bell-mouthed than
they were at first. Another lap used for the same purpose — and
which produces better results — is made by turning a piece of cop-
per, brass, or cast iron to fit the hole and splitting it longitudinally
for some distance from the end. Loose emery is sprinkled over it,
LAPPING 233
with lard oil for a lubricant, and a taper wedge is driven into the
end for adjustment as the lap wears.
For lapping common driU bushings, cam rolls, etc., in large quan-
tities, where a little bell-mouthing can be allowed, and yet a reason-
ably good hole is required, a great many shops use adjustable copper
laps made with more care than the above. One way of making
them is to split the lap nearly the whole length, but leaving both
ends soUd. One side is drilled and tapped for spreading screws
for adjustment. Either one screw half-way down the split may be
used or two screws dividing the split into thirds. Another and
better means of adjustment is to drill a small longitudinal hole a
little over half the length of the lap, enlarge it for half its length,
and tap the large end for some distance. This is done before split-
ting. Into this hole a long screw with a "taper point is fitted so that
when tightened it tries to force itself into a small hole, thus spread-
ing the lap.
For nice work there is nothing better than a lead lap. Lead charges
easily, holds the emery firmly and does not scratch or score the work.
It is easy to fit to the work and holds its shape weU for light cuts.
Under hard usage, however, it wears easily. For this reason, while
laps for a single hole or a special job are sometimes cast on straight
arbors, where much lapping is done it is customary to mold the laps
to taper arbors with means for a slight adjustment. After any exten-
sive adjustment the lap will be out of true and must be turned off.
All o£ these laps, as shown in Fig. 2, are to be held by one end in
a lathe chuck, and the work run back and forth on them by hand,
or by means of a clamp held in the hand. If a clamp is used care
should be taken not to spring the work.
How to Do Good Lapping
There are several points which must be taken into consideration
in order to get good results in lapping holes. The most important
is that the lap shall always fill the hole. If this condition is not com-
phed with the weight of the work and the impossibility of holding
it exactly right will cause it to lap out of round, or if it is out of round
at the start the lap mil be free to follow the original surface. If the
lap fits, it will bear hardest on the high spots and lap them off. Next
in importance to getting a round hole is to have it straight. To
attain this end the lap should be a little longer than the work, so
that it will lap the whole length of the hole at once, and not have a
tendency to follow any curvature there may be in it. What is known
as bell-mouthing, or lapping large on the ends, is hard to prevent,
especially if the emery is sprinkled on the lap and the work shoved
on it while it is running. The best way to avoid this condition when
using cast-iron or copper laps, which do not charge easily, is to put
the emery in the slot, near the center of the lap, and after the work
is shoved on squirt oU in the slot to float the emery. Then, when
the lathe is started the emery wiU carry around and gradually work
out to the ends, lapping as it goes. Where lead is used the emery
can be put on where it is desired to have the lap cut and roUed in
with a flat strip of iron. It will not come out easily, so will not spread
234 GRINDING AND LAPPING
to any extent, and it is possible with a lap charged in this manner
to avoid cutting the ends of the hole at all. The work should always
be kept in motion back and forth to avoid lumping of the emery
and cuttings which will score grooves in the work.
Ring Gage and Other Work
Ring gages are lapped with a lead lap. They are first ground
straight and smooth to within .0005 inch of size, and then, when
lapped, are cooled as well as cleaned, before trying the plug, by
Fig. 3. — A Lap for Plugs
placing them in a pail of benzine for a long enough time to bring
them down to the temperature of the room. Some shops leave a
thin collar projection from each side around the hole, so that, if there
is any bell-mouthing, it will be in these collars, which are ground
off after the lapping is done.
Other metals are lapped in this same manner, except that the
abrasive is different. Cast iron is lapped with emery, but ch'arges
to some extent. This charging can be taken out without changing
the work materially by rubbing it by hand with flour of emery cloth.
In lapping bronze or brass, crocus and Vienna lime are used. Crocus
is used with a cast-iron or lead lap, and the charging is removed by
running the work for a few seconds on a hardwood stick which fits
the hole. Unslaked Vienna lime, freshly crushed, is used with a
lead or hardwood lap, and does not charge. It does a nice job, but
is very slow, and is only used in watch factories.
For lapping plug gages, pistons, and other cylindrical articles, a
cast-iron lap is usually used, split and fitted with a closing and a
spreading screw, as shown in Fig. 3. Sometimes, where a very fine
finish is required, or where the work is not hardened, the hole is
made larger than the work, and a lead ring cast into it.
DIAMOND POWDER IN THE MACHINE SHOP
The diamond used for this purpose, costing 85 cents per carat, is
an inferior grade of diamond, not so hard as the black diamond used
for drills and truing emery wheels, and not of a clear and perfect
structure to permit it to enter the gem class. Many are a mixed
black and white, others yellow and some pink; many are clear but
flaky. Then there is the small debris from diamond cutting, which
is reduced to powder and sells somewhat cheaper; but some find
it more economical to use the above and powder it themselves, as
the debris from diamond cutting is of a flaky nature, and does not
charge into the lap so well.
DIAMOND POWDER IN THE MACHINE SHOP 235
Assuming there is 25 carats to reduce to powder, proceed as follows:
Into a mortar, as shown at Fig. 4, place about 5 carats, using an
8-ounce hammer to crush it. It takes from 3 to 4 minutes' steady-
pounding to reduce it to a good average. Scrape the powder free
from the bottom and the sides and empty into one half pint of oil.
The oil used is the best olive oil obtainable, and is held in a cup-
shaped receptacle that wiU hold a pint and one half. The 25 carats
being reduced to powder, and in the oil, stir it until thoroughly mixed,
and allow to stand 5 minutes; then pour off to another dish. The
diamond that remains in the dish- is coarse and should be washed
in benzine and allowed to dry, and should be repounded, unless
extremely coarse diamond is desired. In that case label it No. o.
Now stir that which has been poured from No. o, and allow to stand
10 minutes. Then pour off into another dish. The residue will
be No. I. Repeat the operation, following the table below.
The settlings can be put into small dishes for convenient use,
snough oil sta>ang with the diamond to give it the consistency of
paste. The dishes can be obtained from a jewelers' supply house.
Table for Settling Diamond Powder
To obtain No. o — 5 minutes. To obtain No. 3 — i hour.
To obtain No. i — 10 minutes. To obtain No. 4 — 2 hours.
To obtain No. 2 — 30 minutes. To obtain No. 5 — 10 hours.
To obtain No. 6 — until oil is clear.
Diamond is seldom hammered; it is generally rolled into the
metal. For instance, several pieces of wire of various diameters
charged with diamond may be desired for use in die work. Place
the wire and a small portion of the diamond between two hardened
surfaces, and under pressure roll back and forth until thoroughly
charged. No. 2 diamond in this case is generally used. Or one can
form the metal any desired shape and apply diamond and use a roll,
as Fig. 6, to force the diamond into the metal. This is then a 'file
which will work hard steel, but the moment this diamond file, or lap,
is crowded it is stripped of the diamond, and is consequently of no
use. It is to be used with comparatively light pressure.
Diamond Laps
Copper is the best metal. It takes the diamond readily, and
retains it longer than other metals; brass next, then bessemer steel.
The latter is used when it is wished to preserve a form that is often
used.
For sharpening small, flat drills, say 0.008 to o.ioo, a copper lap
mounted on a taper shank, as in Fig. 5 and charged on the face with
No. 2 diamond, using pressure on the roll, makes a most satisfactory
method of sharpening drills. The diamond lasts for a long time if
properly used, and there is no danger of drawing the temper on the
drill. It is much quicker than any other method of sharpening.
To charge the lap use the roll. Fig. 7, supported on a T rest press-
ing firmly against the lap, being careful to have the roll on the
center; otherwise instead of charging the lap it will be grinding the
236
GRINDING KNB LAPPING
roll. The diamond may be spread either on the lap or the roll, and
the first charging usually takes twice the amount of diamond that
subsequent charging takes. To avoid loss of diamond, wash the
FIG.5U
FIG. t)
FIG. 7
FIG. 4
Diamond Lap Tools
lap in a dish of benzine kept exclusively for that purpose. This can
be reclaimed by burning the metal with acids, and the diamond can
be. resettled.
For the grinding of taper holes in hard spindles or for position
work in hard plates, where holes are too small to allow the use of
emery wheels, No. i diamond does the work beautifully. Or if it
is wished to grind sapphire centers or plugs as stops, etc., a bessemer
lap made in the form of a wheel and charged with diamond on the
diameter does the work nicely.
Nos. 5 and 6 diamond are used on boxwood laps, mounted on
taper plugs or chucks, and the diamond smeared on with the finger.
The lap is run at high speed and used for fine and slow cutting
which also gives a high pohsh.
REAMER AND CUTTER GRINDING
Reamer Clearances
After constant experimenting for a period of more than a year,
the Cincinnati Milling Machine Company succeeded in establishing
tables for four styles of reamers for obtaining what they consider to
be the best clearances, the object being to grind clearances on reamers
which would ream the greatest number of smooth holes with a mini-
mum amount of wear. The four styles of reamers are as follows:
Hand reamers for steel, hand reamers for gray iron and bronze, chuck-
ing reamers for gray iron and bronze, chucking reamers for steel.
The company uses adjustable blade reamers almost exclusively, all of
which are ground in the toolroom on their universal cutter and tool
grinder. High speed steel reamers cUng to nickel steel and do not
cut it as well as carbon steel.
REAMER AND CUTTER GRINDING 237
Fig. I is a cross-section of a hand reamer. Two clearance lines,
A and B, are ground on the blades, a being the cutting clearance
and b the second clearance called for in the table. The object of
giving the adjustment for the second clearance so minutely is to pro-
vide a proper width of land, which equals .025 inch on all hand reamers
for gray iron or bronze, and 0.005 i^^ch on hand reamers for steel.
Fig. I . — Cross-section of Hand Reamer
Chucking reamers for gray iron and bronze have, in this system, 23-
degree beveled ends as shown in Fig. 2, and are provided with two
clearances along the blades, for which the settings are given in Table
3. The beveled ends have only one clearance which is equal to the
second clearance given in Table 3. Fig. 3 shows a chucking reamer
for reaming steel. In these reamers the blades are circular ground
to the exact size of hole to be reamed and without clearance, the 45-
I'v^
Fig. 2. — Chucking Reamer Fig. 3. — Chucking Reamer
Blade for Gray Iron and Bronze Blade for Steel
degree beveled ends only having clearance as given in Table 4. On
all reamers of this style the blades are ground from .015 to .020 inch
below size half of their length toward the shank end.
In grinding the clearances for the various kinds of reamers as
given in Table i, 2, and 3, the tooth rest is held stationary on the
emery wheel hea4 of the grinder, while in grinding the 45-degree
beveled ends on the chucking reamers for steel, the tooth rest is
supported from the grinder table and travels with the work. The
front end of the hand reamer blades are tapered about 0.004 pei
inch. The back ends of the blades are also slightly tapered to pre-
vent injuring the holes when backing the reamer out.
238
GRINDING AND LAPPING
REAMER CLEARANCE
Set Tooth Rest
Below Work
Ground with Cup Wheel 3"
dia.— Tooth Rest to be Set Central
Holding Centers.
with Emery Wheel Spindle. Set Work holding Centers above
Amount given
Emery Wheel Center by
\mount given below in Tables No.
Below in Table
1-2 and 3
No. 4
TABLE I
TABLE 2
TABLE 3
TABLE 4
Hand Reamer for Steel
Hand Reamer
Chucking
Chucking Ream-
Cut'g
Clearance Land
for Cast Iron
Reamer for
ers for Steel Cir-
.006 Wide
and Bronze
Cast Iron and
cular Ground
Cut'g Clear-
Bronze Cut'g
ance Land
C 1 e a r a n ce
.025 Wide
Land .025
Wide
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.077
•237
45
.240
Mount Tooth R(
;st on Emery Whe
el Head
Mount Tooth Rest
on Table of Machine
REAMER AND CUTTER GRINDING
239
REAMER CLEARANCE
Set Tooth Rest
Below Work
Ground
vith Cup Wheel 3"
dia.— Tooth Rest to be Set Central
Holding Centers.
with E
mery Wheel Spindle. Set Work holding Centers above
Amount given
Emery Wheel Center by Amount given below in Tables No.
Below in Table
1-2 and 3
No. 4
TABLE I
TABLE 2
TABLE 3
TABLE 4
Hand Reamer for Steel
Hand Reamer
Chucking
Chucking Ream-
Cut'g
Clearance Land
for Cast Iron
Reamer for
ers for Steel Cir-
.006 Wide
and Bronze
Cast Iron and
cular Ground
Cut'g Clear-
Bronze Cut'g
ance Land
Clearance
.025 Wide
Land .025
Wide
M4,
"O D
s>fio
'O aj
W 0
"^ 0
C"«
M 0
0 u
c z
C 0
C 0
C 0
c S
0 0
CUD
■5 ^
0 a
■•3 a
R c
"z; ^
0 a
•■= B'si
B
.^1
3 M
0^
r^2
3 d
si
3 5 c
t/2
fa
fa
fa
fa
fa
fa
<
fa
^\K
.012
.172
.06s
.225
.077
.237
45 Degrees
.240
2^
.012
.172
.070
.230
.080
.240
45
.240
2\r
.012
.172
.070
.230
.080
.240
45
.240
3 , .
.012
.172
.072
.232
.080
.240
45
.240
H<.
.012
.172
.072
.232
.080
.240
45
.240
Al
.012
.172
•075
•235
.083
.240
45 "
.240
3p
X)I2
.172
•07s
•235
.083
.243
45
.240
H
.012
.172
.078
.238
.083
.243
45 "
•245
W^
.012
.172
.078
.238
.087
•243
45
•245
.012
.172
.081
.241
.087
•247
45
.245
W"
.012
.172
.081
.241
.090
.247
45 "
.245
.012
.172
.084
•244
.090
.250
45
.250
^K
.012
.172
.084
.244
.090
.250
45
.250
si "
.012
.172
.0S7
.247
•093
•253
45
.250
t''
.012
.172
.087
•247
■093
.253
45 "
.250
.012
.172
.090
.250
.097
.257
45
•255
^W„
.012
.172
.090
.250
.097
.257
45 ''
•255
^\ ,
.012
.172
•093
•253
.100
.260
45
.255
3iC
.012
.172
•093
•253
.100
.260
45 "
.255
4
.012
.172
.096
.256
.104
.264
45 "
.260
4?%
.012
.172
.096
.256
.104
.264
45
.260
a\ "
.012
.172
.096
.256
.104
.264
45
.260
4iV'
.012
.172
.096
.256
.106
.266
45
.260
A\"
.012
.172
.096
.256
.106
.266
45 "
.265
4tV'
.012
.172
.096
.256
.106
.266
45 "
.265
4l'
.012
.172
.096
.256
.108
.268
45 "
.265
4iV'
.012
.172
.096
.256
.108
.268
45 "
.265
Ah"
.012
.172
.100
.260
.108
.268
45 "
.265
^C'
.012
.172
.100
.260
.108
.268
45
.265
.012
.172
.100
.260
.110
.270
45
.270
C"
.012
.172
.100
.260
.110
.270
45
.270
.012
.172
.104
.264
.114
•274
45
.275
4?«'
.012
.172
.104
.264
.114
.274
45 "
.275
41
.012
.172
.106
.266
.116
.276
45 "
.275
A\%"
.012
.172
.106
.266
.116
.276
45 "
.275
^3 "
.012
.172
.110
.270
.118
.278
45 "
.275
5I "
.012
.172
.118
278
Mount
Tooth Re
St on En:
lery Whe
dHead
Mount To
on Table of
oth Rest
Machine
240
GRINDING AND LAPPING
liK}^^:.it
<~
--JX
:>;:%.
'lil
r^ ,
ilii\^x^^
.^is
Z-t i
Eu^%^A C 1 j
^^i
r^-'T""
1 ~^MV B-J7_;
•meyy:
1 W(jri
1 -',--■■.■:■'■■/
/ •
.^fceej.:
1 .-:•..■-■/
/ 1
■^\ v —
-0 -■ ;■ -y
t^ Work
V/^^s^^
■^.^^
V/v
Tooth Kest
Tooth Best
^-Nx-
Cup Wheel Clearance Table
Disk Wheel Clearance Table
For setting tooth rest to obtain
Giving distance B for setting
5° or 7° clearance when grinding
work centers and tooth rest be-
peripheral teeth of milling cutters
low center of wheel spindle to
with cup-shaped wheel. Tooth
obtain 5° or 7° clearance with
rest is set below work centers as
wheels of different diameters
at A , the distance being found in
when grinding with periphery of
.the table below.
disk wheel.
Dia.
For 5°
For 7° "
Dia. of
Emery
Wheel
Inches
For 5°
For f
Cutter
Clearance
Clearance
Clearance
Clearance
Inches
A =
A =
B =
B =
i
.Oil
.015
2
•0937
.125
f
.015
.022
2i
.099
.141
h
.022
.03Q
2\
.110
.156
t
.028.
•037
2f
.125
.172
1
•033
.045
3
.132
.187
I
•037
.052
3i
.143
.203
I
.044
.060
z\
.154
.219
li
.055
•075
Z\
.165
•234 •
l^
.066
.090
4
.176
.250
If
.077
.105
4i
.187
.265
2
.088
.120
4i
.198
.281
2i
.099
.135
4f
.209
•297
A
.110
.150
5
.220
.312
2f
.121
.165
5i
.231
.328
3
.132
.180
5^
.242
•344
z\
.154
.210
5f
.253
•359
4
.176.
.240
6
.264
.375
4^
.198
.270
6i
.275
•390
5
.220
.300
6i
.286
.406
51
.242
'7>Zo
61
.297
.421
6
.264
.360
7
.308
•437
OILSTONES 241
OILSTONES AND THEIR USES
Natural Stones
The following particulars regarding the well-known Arkansas and
Washita stones are given by the Pike JManufacturing Company:
Arkansas stones are made from rock quarried in the Ozark moun-
tains of Arkansas, and are prepared for commercial purposes in two
grades, hard and soft.
Hard Arkansas is composed of pure silica and its sharpening
qualities are due to small, sharp-pointed grains, or crystals, of hex-
agonal shape, which are much harder than steel and wiU, therefore,
cut away and sharpen steel tools. The extreme fineness of texture
makes this stone, of necessity, a slow cutter, but in the very density
of the crystals of which it is composed lies its virtue as a sharpener.
Soft Arkansas stone is not quite so fine-grained and hard as the
hard Arkansas, but it cuts faster and is better for some kinds of
mechanical work. It is especially adapted for sharpening the tools
used by wood carv^ers, file makers, pattern makers, and aU workers
in hard wood.
Washita stone is also found in the Ozark mountains in Arkansas
and is similar to the Arkansas stone, being composed of nearly pure
silica, but is much more porous. It is known as the best natural
stone for sharpening carpenters' and general wood workers' tools.
This stone is found in various grades, from perfectly crystallized
and porous grit to vitreous flint and hard sandstone. The sharp-
ness of the grit depends entirely upon its crystallization, the best
oilstones being made from very porous crystals.
In addition to the regular rectangular sections, natural stones are
made in such shapes as square, triangular, round, flat, bevel, dia-
mond, oval, pointed, knife edge.
Artificial Oilstones
Artificial oilstones are manufactured in a multitude of shapes and
sizes and are adapted for sharpening all kinds of tools. Such stones
ard made by the Norton Company of alundum and crystolon, the
former being known as India oilstones, the latter as crystolon sharp-
ening stones. Similar shapes are manufactured by the American
Emery Wheel Works, and the Carborundum Company also makes
such stones in great variety.
The stones are made in three grades or grits, coarse, medium and
fine. The coarse stones are used in machine shops for sharpening
very dull or nicked tools, machine knives, and for general use where
fast cutting is desired.
Medium stones are sharpening mechanics' tools in general, more
particularly those used by carpenters and in wood-working shops.
Fine stones are adapted for engravers, die workers, cabinet makers
and other users of tools requiring a very fine, keen-cutting edge.
Of the great variety of shapes and sizes a number adapted espe-
cially for machine shop purposes are illustrated half size in Fig. i . Of
these, Nos. o, i, i|, 2, 24 and 29 are for sharpening lathe and planer
242
GRINDING AND LAPPING
tools, and for use after grinding; Nos. 23, 25, 56 and 56^ for reamers;
Nos. 13, 14 and 15 for taps; Nos. 4, 5, 6, 7, 8, 9, 10, 11, 12 and 26
for dies.
No.O - 8x2x1
No.29 -e'xs'xi'
N0.2
Fig. I. — Shapes of Oilstones
A few shapes and sizes for curved-edge wood-working tools are Nos.
ro, iij 12, 13, 14, 15, in Fig. i. Rectangular shapes for straightedge
SHAPES OF OILSTONES 243
tools like chisels, plane bits, planer knives, scrapers, paper-cutting
knives and other tools with broad flat edges are Nos. o, i, i^, 2, 24,
29, in Fig. I.
No.58 No.51
Fig. 2. — Shapes of Oilstones
Fig. 2 shows some of the sizes and shapes particularly adapted for
mold and die work, watch and clock makers' tools, etc. Other
244 GRINDING AND LAPPING
shapes suitable for such purposes are shown by Nos. 4, 5, 6, 7, 8, 9
and 26 in Fig. i and No. 51 in Fig. 2.
How to Care for Oilstones
Like anything else, an oilstone can be ruined' by wrong treatment
and lack of care.
There are three objects to be attained in taking good care of an
oilstone: first, to retain the original life and sharpness of its grit;
second, to keep its surface flat and even; third, to prevent its glazing.
To retain the original freshness of the stone, it should be kept
clean and moist. To let an oilstone remain clry a long time, or
expose it to the air, tends to harden it. A new natural stone should
be soaked in oil for several days before using. If an oilstone is kept
in a dry place (most of them are) it should be kept in a box with
closed cover, and a few drops of fresh, clean oil left on it.
To keep the surface of an oilstone flat and even simply, requires
care in using. Tools should be sharpened on the edge of a stone as
weU as in the middle to prevent wearing down unevenly, and the
stone should be turned end for end occasionally.
To restore an even, flat surface grind the oilstone on the side of a
grindstone or rub it down with sandstone or an emery brick.
To prevent an oilstone from glazing requires merely the proper
use of oil or water.
The purpose of using either oil or water on a sharpening stone is
to float the particles of steel that are cut away from the tool, thus
preventing them from fiUing in between the crystals and causing the
stone to glaze.
AU coarse-grained natural stones should be used with water. Use
plenty of it.
On medium and fine-grained natural stones and in all artificial
stones, oil should be used always, as water is not thick enough to
keep the steel out of the pores.
To finrther prevent glazing, the dirty oil should always he wiped
off the stone thoroughly as soon as possible after using it. This is
very important, for if left on the stone, the oil dries in, carrying the
steel dust with it. Cotton waste is one of the best things to clean a
stone with, and is nearly always to be found in a shop.
If the stone does become glazed or gummed up, a good cleaning
with gasolene or ammonia will usuaUy restore its cutting qualities, but
if it does not, then scour the stone with loose emery or sandpaper
fastened to a perfectly smooth board.
Never use turpentine on an oilstone for any purpose.
SCREW MACHINE TOOLS, SPEEDS
AND FEEDS
BOX TOOLS AND CUTTERS
The general principles of two types of box tools using respectively
tangent and radial cutters are represented in Figs, i and 2. The
former type is generally used for roughing and the latter for finishing.
The tangent cutter in the type of box tool shown in Fig. i lies in a
slot formed parallel to the bottom of the box but at an angle, usually
Cutter
Fig.
■Roughing Box Tool with
Tangent Cutter
cen degrees, with the front of the box, thus giving the desired rake
at the cutting point. Finishing cutters of the type in Fig. 2 are
Straight on the end, located square with the work and ordinarily
ground as indicated to give 7 to 10 degrees front clearance for steel
and 5 to 8 degrees for brass.
The tangent cutter is sharpened by grinding on the end, and com-
pensation for the grindii:g away of the metal is made by adjusting
the cutter forward, v/hereas in the radial type of cutter in Fig. 2,
frequent sharpening cannot be done without resulting in lowering
the cutting edge of the tool below the center of the work, unless a
substantial part of the tool be sacrificed. The radial tool, however,
is easily ground accurately on face a, which is the edge gover'aing the
finish; while the corresponding face on the tangent tool is rather
difficult to grind so as to produce as smooth work.
24s
246 SCREW MACHINE TOOLS, SPEEDS AND FEEDS
The sizes of steel recommended for box-tool cutters are as follows:
For box tools used for stock diameters up to jV inch, i\ inch square;
up to f inch diameter, 3% inch square; ujf to J inch diameter, \ inch
square; up to f inch diameter, y\ inch square; up to i inch diameter,
f inch square; up to ij inches diameter, J inch square.
HOLLOW MILLS
The teeth of hollow mills should be radial or ahead of the center.
With the cutting edge ahead of the center, as in Fig. 3, the chips as
produced are caused to move outward away from the work and pre-
vented from disfiguring it. With the cutting edge below the center,
rough turning will result. With the cutting edge greatly above the
center, chattering occurs. About one tenth of the cutting diameter
is a good average amount to cut tlie teeth ahead of the center.
7° to 10 for Steel
5° to 8°for Brass
Fig. 2. — Finishing Box Tool with
Radial Cutter
When the chips produced from any turning or boring cut cur!
nicely, it is indicative of a free cutting action; but these chips are
very troublesome on the automatic screw machine. In making hollow-
mills for the automatic, part or all of the rake to the cutting edge is
generally sacrificed.
The table under the hollow mill in Fig. 3 gives proportions of
mills from xV to f diameter, showing the amount to cut the teeth
ahead of the center, the taper of the hole, etc.
DIES AND TAPS
247
D =
■ Finishing. . "1
. Roughing . J
.072
.104
•135
.166
ft
.197
.229
.26
.291
ft
.322
1
•385
.510
1
635
f
.760
L =
i
i
^
T^S
f
1
ft
ft
4
f
1
i-
I
10
.006
.009
.012
.015
.019
.022
.025
.028
•031
.038
.050
.063
.075
I =
1%
fs
fs
A-
ft
1
f
i
1
ft
ft
H
ii
0 =
1
1
1
t
1
f
f
1
1
I
i\
If
if
Fig. 3. — Hollow Mill Dimensions
DIES AND TAPS
It is good practice in making spring screw dies to either hob out
the thread with a hob tap 0.005 to 0.015 i^ch over-size, according
to size, and in use to spring the prongs to proper cutting size by a
clamping ring, or to tap the die out from the rear with a hob tap
tapering from y^g inch to J inch per foot, leaving the front end about
0.002 inch over cutting size, and in this case also to use a clamping
ring. Both of these schemes are for the purpose of obtaining back
clearance and are effective. Of the two the use of the taper hob is
to be preferred.
248 SCREW MACHINE TOOLS, SPEEDS AND FEEDS
Spring Die Sizes
The table of dimensions for spring screw dies, Fig. 4, should proye
of service, particularly for steel. For brass the cutting edge is
radial, thus eliminating dimension A. The width of land at bottom
of thread is usually made about j outside diameter of cut, the milling
between flutes being 70 degrees, leaving 50 degrees for the prong in
the case of three-flute dies.
Taper of Tap=H per Ft.
Small Sizes of Dies
(Over all Dimensions Given in Sketch)
D =
rV
f
A
i
A
No.
3
4
6
8
10
12
Threads P. I. =
10
64
.003
40
.012
32
.019
20
.025
18
.031
56
.010
40
.011
32
.014
24-
32
.016
24-
32
0.19
24-
32
.021
L =
t\
3^
f
h
i
aV
i
3^.
t\
H
f
Sizes | to 1 Inch
D =
ftoi
Hof
f to I
Th' s P.I. =
Std.
Std.
Std.
A =
D ^ ID
D ^ 10
D ^ 10
L =
f
x"
li
O.S. Dia.
I"
li
if
Length
2"
2^
2Y
Fig. 4. — Spring Die Dimensions
Sizing Work for Threading
In boring holes previously to tapping they should be somewhat
larger than the theoretical diameter at bottom of thread, as the
crowding action of the tap will cause the metal to flow som^e and
compensate for this. Where no allowance is made, frequent tap
breakage is liable to occur and torn threads in the work also. On
TAP LENGTH AND NUMBER OF LANDS
249
external work it is for the same reasons advisable to turn the work
undersize and the following table gives good average allowances for
both internal and external work.
Allowances for Threading in the Screw Machine
Threads
per Inch
External Work
Turn Undersize
Internal Work
Increase Over Theoretical
Bottom of Thread
28
0.002
0.004
24
0.002
0.0045
22
0.0025
0.005
20
0.0025
0.0055
16
0.003
0.006
14
0.003
0.0065
13
0.0035
0.007
. 12
0.0035
0.007
II
0.0035
0.0075
ID
0.004
0.008
9
0.004
0.0085
8
0.0045
0.009
7
0.0045
0.0095
6
0.005
O.OIO
Tap Length and Number of Lands
The number of teeth in taps and the width of land should be
regulated by the diameter and pitch of work as well as the nature of
the material being cut. On fine threads, where a drunken thread is
to be insured against, more teeth are required than on a coarser pitch
of the same diameter. A good average number of teeth on taps for
United States standard threads is given in the following table. With
Outside Dia.
No. of Flutes
Width of Land
A
4
6^
i
4
tV
t\
4
f
4
J^
T^
4
i-i
^
4
i
f
4
'h
f
4
i
4
3V
I
4
i
li
4
A
too few teeth and too short land very little support is afforded and
this may cause chattering; too much land in contact causes heat due
to excessive friction, welding of chips and torn threads.
250 SCREW MACHINE TOOLS, SPEEDS AND FEEDS
^^''
/ /
/ /
ff
tt
//
//
i
1 *^
•0
//
1
\
/ /
ix.
^
FORMING TOOLS
251
FORMING TOOLS
The two types of forming cutters commonly used in the screw
machine are shown in Figs. 5 and 6. The circular forming cutter in
Fig. 5 is usually cut away from J to -^^ inch below center to give
suitable cutting clearance and the center of the tool post on which
it is mounted is a corresponding amount above the center of the
machine, so that the cutting edge of the circular tool is brought on
Fig. 5. — Circular Forming Tool
the center line of the work. The relative clearance ordinarily
obtained by circular cutters and dovetail tools of the type shown in
Fig. 6, is indicated in Fig. 7. It is obvious that with a given material
the larger the diameter of the work the greater the angle of clearance
required. Clearance angles are seldom less than 7 degrees or over
12 degrees.
The diameter of circular forming tools is an important matter for
consideration. A small diameter has a more pronounced change of
t
Fig. 6. — Dovetail Forming Tool
clearance angle than a large diameter. In fact, when of an exceed-
ingly large diameter the circular tool approaches in cutting action
the dovetail type of tool which is usually provided with about 10
degrees clearance. Circular tools usually range from about if to
3 inches diameter, depending upon the size of machine in which
they are used.
252 SCREW MACHINE TOOLS, SPEEDS AND FEEDS
Getting the Tool Diameters at Different Points
In order to make a circular or a dovetail type of tool so that
the contour of its cutting edge is such as to produce correct work, the
amount a circular tool is cut below center, as at c in Fig, 8, and the
clearance angle of a dovetail tool as at A' , Fig. 7 must be known.
Thus, referring to Fig. 8, the forming tool shown cuts two dififerent
diameters on the work, the step between being represented by dimen-
sion a. To find -depth / to which the forming tool must be finished
on the cent^ line to give the correct depth of cut a in the work (the
Tool cut out here
after Forming
To suit amount Auto-
matic Tool Holder is"
above Center.
Master Tool
Fig. 10. — Finishing a Circular Tool
cutter being milled below center an amount represented by c) the
following formula may be applied:
Suppose the depth of cut in the work represented by o to be 0.152';
the radius g of the forming cutter i inch; the distance c which the
forming tool is milled below center, x\ inch. Applying the above
formula to find/ and substituting the values just given for the letters
in the formula we have/ = i— Vi + .0231 - (.304 \/i — • 03516)
= I - V I + .0231 - (.304 X .9823)
= I - \/ .724485 = I — .8512 = .1488
Then/ =.1488
DOVETAIL TOOL DEPTHS
253
Dovetail Tool Depths
If a similar piece of work is to be formed with a dovetail type of
cutter, the distance T, Figs. 7 and 9, to which it is necessary to plane
the tool shoulder in order that it may cut depth a correctly in the
work, is found by the formula: T = a (cosine A'). As 10 degrees
is the customary clearance on this form of tool, the cosine of this
angle, which is .98481, may be considered a constant, making refer-
ence to a table of cosines unnecessary as a rule. Assuming the same
depth for a as in the previous case, that is .152 inch, and multiplying
by .98481, gives .1496 inch as the depth of T to which the tool must
be planed.
Dovetail
Cutter Blank
Fig. II. — Finishing a Dovetail Forming Tool
While it frequently is necessary or advisable to determine by
calculation the dimension computed in the preceding examples, in
the majority of cases when making a cutter with a master tool of
the same outline as the model, the correct form in the circular cutter
is obtained automatically by dropping the master tool to the same
distance below the lathe center as the circular cutter is to be milled
off center and then feeding it in to finish the cutter. This procedure,
shown in Fig. 10, assures the correct shape at all points being pro-
duced on the exact working plane of the cutter. Similarly, in finish-
ing a dovetail cutter in the planer or shaper, the master tool may be
set as in Fig. 11 at the same angle with the cutter (usually 10 degrees)
as the latter will afterward be applied to the work.
254 SCREW MACHINE TOOLS, SPEEDS AND FEEDS
CIRCULAR TOOL FOR CONICAL POINTS
When a circular cutter is to be mad^ for forming a conical surface*
on a piece as in Fig. 1 2, a master tool of the exact angle required on
the work may be used for finishing the cutter in the same way as the
tool in Fig. 9 is applied; that is, the master is to be dropped below
center the amount the cutter center is to be above the work center
when in operation. The distance is represented by A in Fig. 12.
Another method, which avoids the necessity of making a master tool,
is to set the compound rest of the lathe to the exact angle required
(in this case 30 degrees with the center line) and with a horizontal
Fig. 12. — Circular Forming Tool for Conical Points
cutting tool set at distance D below center, turn off one side of the
cutter blank and then set the compound rest around the other way
and face off the other side. If desired a similar method may be
followed for grinding the forming cutter after hardening. The
arbor carrying the cutter should be located either above or below
the grinding wheel a distance equal to D where D equals
the depth the cutter is milled below center, r the radius of the cutter,
and R the radius of the emery wheel. Assuming D to be .187 (y^g)
inch; R, 2.5 inches; and r, i inch, the vertical distance between centers
of forming tool and grinding wheel centers would equal .187 '—
= .187 (3.5) = .6562 (fl) inch.
DIAMETERS OF FORMING TOOLS
255
FINDING DIAMETERS OF CIRCULAR
FORMING TOOLS
In making circular forming tools it is oftentimes desirable to check
the finished tool or finish a tool by grinding. It may also be advan-
tageous to know the exact diameter a tool should be turned while
making it, in order that calipering may be more convenient and
certain. Methods of computing the diameter at different points are
given on page 252, but in many cases of this kind the following
tables win greatly facilitate matters, particularly when making
circular forming tools for
Brown & Sharpe automatic
screw machines:
Suppose, for example, we
have a piece to make hke Fig.
13, on the No. 2 BrouTi &
Sharpe automatic screw ma-
chine. The largest diameter
of the circular forming tool
would produce the smallest
diameter of the piece, which is 0.250 inch. The difference between
this 0.250-inch diameter and the step of the 0.750-inch diameter
is (0.750 — 0.250 inch) -r- 2 = 0.250 inch.
The largest diameter of the circular forming tool for the No. 2
machine is 3 inches, which corresponds to a radius of 1.49998 inches
with a base Hne of 1.479 ii^ch for the triangle completed by the per-
pendicular joining the cutting line of the tool with the parallel line
passing through the center of the tool.
The h>Tpothenuse of the triangle is formed by the radius joining
the intersection of the base line and the circumference of the tool
as in Fig. 14. Subtracting 0.250 inch from 1.479 inches we have
1.229 inches, which, in Table 4, corresponds to a radius of i. 2541 7
inches, and multiplying by 2 gives a diameter of 2.50834 inches,
to which to turn the cutter to correctly form the 0.750-inch diameter
on the piece. Fig. 13.
Considering the largest diameter of the piece and taking the height
The piece to be made
of the second step above the first diameter, we have
0.938 — 0.25
0.344 inch, and subtracting from 1.479 = 1.135 for the base line,
which, in Table 4, corresponds to a radius of 1.16221. Multiplying
by 2 gives a diameter of 2.3244 to turn the cutter to in order to pro-
duce the 0.938-inch diameter on the work. Tables 2, 3 and 4 are
for cutters of the dimensions given in Table i.
These tables are figured in steps of 0.00 1 inch for the capacity of
the machines. A difference of a fractional part of a thousandth can
be added to the radius if the step is a part of a thousandth over the
base-line figures, which are given in even thousandths. For illus-
tration: Say the base-line figure is 1.4765 inches. In the table
1.476 inches corresponds to a radius of 1.49702; add 0.0005 inch to
1.49702 and the radius will be as near correct as it is practicable to
make a cutter.
256 SCREW MACHINE TOOLS, SPEEDS AND FEEDS
Table i. — Dimensions of Cutters for
B. & S. Automatic Screw Machines
Mach.
No.
Approx.
Diam.
Max.
Radius
Max.
Base Line
Distance Above
or Below Center
2
0
00
%
1.49998"
1. 1 2474"
0.87497"
1.479"
1. 109"
0.866"
0.250"
0.1875"
0.125"
Fig. 14
Table 2, — For Finding Diameters of Circular Forming Tools
FOR Brown & Sharpe No. 00 Automatic Screw Machine
No. 00
No. 00
No. 00
No. 00
No. 00
Base
Line
Radius
Base
Line
Radius
Base
Line
Radius
Base
Line
Radius
Base
Line
Radius
.866
.865
.864
.863
.862
.861
.860
i%
.857
.856
.855
■854
.853
.852
.851
.850
'.sis
.847
.846
.845
.844
.843
.842
.87497
.87398
•87300
.87201
.S7102
.87003
.86904
.86805
.86706
.86607
.86508
.86409
.86310
.86211
.86112
.86013
.85914
.85815
.85716
.85617
.85518
.85420
.85321
.S5222
•85123
.841
.840
i%
.837
.836
.835
.834
•833
.832
.831
.830
.829
.828
.827
.826
•825
.824
.823
.822
.S21
.8 20
.819
.81S
.817
.816
.85024
.84925
.84826
•84727
.84628
•84529
•84430
•84332
•84233
.84134
•84035
•83936
•83837
•83738
•83639
.83540
.83442
•83343
•83244
•83145
.83046
fi%
•82750
.82651
.82552
.S15
.814
•813
.812
.811
.810
^807
.806
.805
.804
.803
.802
.801
.800
•799
•798
•797
•796
•795
•794
•793
• 792
.791
• 790
82453
82354
82255
S2156
S2058
81761
81662
81564
81465
S1366
81267
81168
81069
80971
80872
80773
80674
80576
80477
80378
80279
80180
80082
79983
■.788
•787
.786
•785
• 784
• 783
.782
.781
.780
■III
•777
• 776
•775
.774
•773
• 772
.771
.770
'.768
• 767
.766
.765
.764
.79884
•79785
.79686
.79588
•79489
•79390
•79291
•79193
•79094
•78798
.78699
.78600
.78502
.78403
•78304
.78205
.78107
.78008
•77909
•778II
•77712
•77613
•77515
•77416
.763
.762
.761
.760
•759
.758
•757
•756
■755
•754
• 753
•752
•751
• 750
-749
•748
.747
.746
•745
■744
•743
•742
.741
•740
.77317
.77218
.77120
.77021
.76922
.76823
.76725
.76626
.76528
.76429
.76330
.76232
•76133
.76035
•75936
.75837
•75739
•75640
•75541
.75443
•75344
.75246
•75147
.75048
Note. — In the above Table 2 and Tables 3 and 4, it should be
noted, as explained on page 255, that the Base Line dimensions in
the columns under that heading and in the diagram, Fig. 14, are
actually the distance of the cutting edge of the tool from the center
oi the cutter, the latter being used in the machine a certain distance
either above or below the spindle center corresponding to Table i.
The distance from the cutting edge to center is therefore shorter
than the true cutter radius by the amount indicated in the tables.
DIAMETERS OF FORMING TOOLS
257
Table 3. — For Finding Diameters of Circular Forming
Tools for Brown & Sharpe No. o Automatic
Screw Machine
No. 0
No.o
No.o
No.o
IS
0. 0
Base
Line
Radius
Base
Line
Radius
Base
Line
Radius
Bnsp
Line
Radius
Base
Line
Radius
1. 109
1. 12474
1.060
1.07646
1. 010
1.02726
.960
•97813
.910
.92911
1. 108
I-I237S
i.059
1.07547
1.009
1.02627
•959
•97715
.909
•92813
1. 107
1. 12277
1.058
1.07448
1.008
1.02529
•958
•97617
.908
■9271S
1. 106
1.12178
1.057
1.07350
1.007
1.02431
•957
•97519
.907
.92617
1. 105
1. 12079
1.056
1.07252
1.006
1.02332
•956
.97421
.906
.92519
1. 104
1.11981
1.055
1.07153
1.005
1.02234
•955
•97323
.905
.92421
1. 103
1.11882
1.054
1.07055
1.004
1. 02136
•954
.97225
.904
.92324
1. 102
1.11784
I-OS3
1.06956
1.003
1.02038
•953
.97127
.903
.92226
I.IOI
1.11685
1.052
1.06857
1.002
1.01939
•952
.97028
.902
.92128
1. 100
1.11586
1.051
1.06759
I.OOI
1.01841
•951
.96930
.901
.92030
1.099
1.11488
1.050
1.06661
1. 000
1.01743
•950
.96832
.900
.91932
1.098
1.11389
1.049
1.06563
.999
1.01644
•949
.96734
.899
.91834
1.097
1.11291
1.048
1.06464
.998
1.01546
•948
.96636
.898
.91732
i.oq6
1.11192
1.047
1.06366
.997
1.01448
•947
.96538
.897
.91638
1.095
1. 1 1094
1.046
1.06267
.996
1.01349
•946
.96440
.896
.91540
1.094
1. 10995
1 .045
1. 06 1 69
.995
1.01251
.945
.96342
.895
.91442
1.093
1. 10896
1.044
1.06070
.994
1.01153
•944
.96244
.894
•9134s
1.092
1. 10798
1.043
1.05972
•993
1.01055
•943
.96146
■893
.91247
1. 09 1
1. 10699
1.042
1.05874
.992
1.00957
•942
.96047
.892
.91149
1.090
1.10601
1. 041
1.05775
.991
1.00858
.941
.95949
.891
•91051
1.089
I. 10502
1.040
1.05677
•990
1.00760
•940
.95851
.890
•90953
1.088
1. 10404
1.039
1.05578
.989
1.00662
•939
•95753
.889
•9085s
1.087
1. 10305
1.038
1.05480
.988
1.00563
•938
•95655
.888
•90757
1.086
1. 10207
1.037
1.05381
.987
1.00465
•937
•95557
.887
.90660
i.oSs
1.10108
1.036
1.05283
.986
1.00367
.936
-95459
.886
.90562
1.084
1. 10009
1.035
1.05185
.985
1.00269
•935
•95361
.885
.90464
1.083
1. 099 1 1
I.034
1.05086
.984
1.00170
•934
•95263
.884
.90366
1.082
1.09813
1.033
1,04988
.983
1.00072
•933
•95165
.883
.90268
1. 08 1
1.09714
1.032
1.04889
.982
.99974
•932
-95067
.882
.90170
1.080
1.09616
1.031
1.04791
.981
.99875
•931
.94969
.881
•90073
1.079
1. 095 1 7
1.030
1.04693
.980
•99777
•930
•94871
.880
•89975
1.078
1. 094 1 8
1.029
1.04594
.979
•99679
•929
•94773
.879
.89877
1.077
1.09319
1.028
1.04496
.978
•99581
.928
•94675
.878
.89779
1.076
1.09221
1.027
1.04398
.977
•99483
•927
•94577
.877
.89681
I-07S
1.09123
1.026
1.04299
.976
•99384
.926
•94479
.876
.89584
1.074
1.09024
1.025
1.04200
•975
.99286
•925
•94381
.875
.89486
1.073
1.024
1. 04102
.974
.99188
.924
.94283
.874
.89388
1.072
1.08828
1.023
1.04004
.973
.99090
•923
.94185
.873
.89290
1. 071
1.08729
1.022
1.03906
.972
.98991
.922
.94087
.872
.89193
1.070
1.08630
1.02 1
1.03807
.971
.98893
.921
.93989
.871
.89095
1.069
1.08532
1.020
1.03709
.970
•98795
.920
.93891
.870
.88997
1.068
1.08433
1. 019
1.03611
.969
.98697
•919
.93793
.869
.88899
1.067
1-08335
1.018
1.03512
.968
•98559
.918
.93695
.868
.88802
1.066
1.08236
1. 017
1. 03414
.967
.98501
.917
.93597
.867
.88704
1.065
1.08138
1. 016
1.03316
.966
.98402
.916
.93499
.866
.88607
1.064
1.08039
1.015
1.03217
.965
•98304
•915
.93401
.865
.88508
1.063
1.07941
1.014
1.03119
.964
.98206
.914
.93303
.864
.88411
1.062
1.07842
1.013
1.0302 I
.963
.98108
.913
•93205
.863
.88313
1. 06 1
1.07744
1.012
1.02922
.962
.98010
.912
.93107
.862
.88216
I. on
1.02824
.961
•97912
.911
■93009
.86i
.860
•859
.88118
.88020
.87922
258 SCREW MACHINE TOOLS, SPEEDS AND FEEDS
Table 4. — For Finding Diameters of Circular Forming
Tools tor Brov/n & Sharpe No. 2 Automatic
Screw Machine
No. 2
No.
2
No.
2
No.
2
No. 2
Base
Line
Radius j
ase T
.ine
laclius T
ase ^
adius j-
ase p
.ine ^
adius
Base
Line
Radius
1.479
1.49998 I
430 I
45168 I
380 1
40246 I
330 I
35329
1.280
1.30419
1.478
1.49899 I
429 I
45070 I
379 I
40148 I
329 I
35231
1.279
1.30320
1-477
1. 49801 I
428 1
44982 I
378 I
40050 I
328 1
35133
1.278
1.30222
1.476
1.49702 I
427 I
44873 I
377 I
39952 I
327 I
35035
1.277
1.30124
1-475
1.49604 I
426 I
44775 I
376 I
39853 I
326 1
34936
1.276
1.30026
1.474
1-49505 I
425 I
44676 I
375 I
39754 I
32s I
34838
1-275
1.29928
1-473
1.49406 I
424 I
44578 I
374 I
39656 . I
324 I
34740
1.274
1.29830
1.472
1.49308 I
423 I
44479 I
373 I
39558 I
323 I
34641
1.273
1-29732
1.471
1.49209 I
422 I
44381 I
372 I
39459 I
322 I
34543
1.272
1.29633
1.470
1.49110 I
421 I
44282 I
371 I
39360 I
321 1
34445
1.271
I-2953S
1.46Q
1. 4901 2 I
420 I
441 84 I
370 I
39262 I
320 I
34347
1.270
1.29437
1.468
1.48913 I
419 I
44085 I
369 I
39164 I
319 I
34248
1.269
1-29339
1.467
1.48815 I
418 I
43987 I
368 I
39066 I
318 1
34150
1.268
1. 29241
1.466
1.48716 I
417 I
43874 I
367 I
38967 I
317 I
34052
1.267
1.29143
1.46s
1.48618 I
416 I
43790 I
366 I
38869 I
316 I
33954
1.266
1.29045
1.464
1.48519 I
415 I
43090 I
365 I
38770 I
315 I
3385s
1.265
1.28947
1.463
1. 4842 1 I
414 I
43593 I
364 I
38672 I
314 I
337S7
1.264
1.28848
1.462
1.48322 I
413 I
43495 I
363 I
38574 I
313 I
33659
1.263
1.28750
1.461
1.48223 I
412 I
43396 I
362 I
38475 I
312 I
33560
1.262
1.28652
1.460
1.4812s I
411 I
43298 I
361 I
38377 I
311 I
33462
1. 261
1-28554
1-459
1.48026 I
410 I
43199 I
360 I
38279 I
310 I
33364
1.260
1.28456
1.458
1.47928 I
409 I
43100 I
359 I
38181 I
309 I
33266
1-259
1-28358
1-457
1.47829 I
408 I
43002 I
358 I
38082 I
30S I
33168
1-258
1.28260
1.456
1.47731 I
407 I
42905 I
357 I
37984 I
307 I
33069
1-257
i;28i62
1.455
1.47632 I
406 I
42805 I
356 I
3788s I
306 I
32971
1.256
1.28064
1-454
1-47534 I
405 I
42707 I
355 I
37786 I
305 I
32873
1-255
1.27966
1-453
1-47435 I
404 I
42608 I
354 I
37689 I
304 I
32775
1.254
1.27868
1.452
1-47337 I
403 I
42510 I
353 I
37590 I
303 I
32677
1.253
1.27770
I-45I
1-47238 I
402 I
42411 I
352 I
37492 I
302 1
32578
1-252
1.27672
1.450
1.47139 I
401 I
42313 I
351 I
37393 I
301 1
32480
1-251
1-27574
1.449
1.47041 I
400 I
42215 I
350 I
37295 I
300 I
32382
1.250
1.27476
1.448
1.46944 I
399 I
42116 I
349 I
37197 I
299 I
32284
1.249
1.27377
1-447
1.46846 I
398 I
42118 I
348 I
37098 I
298 I
32186
1.248
1.27279
1.446
1.46745 I
397 I
41919 I
347 I
37000 I
297 I
32087
1.247
1.27181
1-445
1.46647 I
396 I
41821 I
346 I
36902 I
296 I
31989
1.246
1.27083
1.444
1.46548 I
395 I
41723 I
345 I
36S04 I
295 I
31891
1-245
1.26985
1-443
1.46459 I
394 I
41624 I
344 I
36705 I
294 I
31793
1.244
1.26887
1.442
1.46351 I
393 I
41526 I
343 I
36607 I
293 I
31695
1-243
1.26789
1.441
1.46253 I
392 I
41427 I
342 I
36509 I
292 I
31596
1.242
1. 26691
1.440
1.46154 I
391 I
41329 I
341 I
36410 I
291 1
31498
1.241
1-26593
1-439
1.46056 I
390 I
41230 I
340 I
36312 I
290 I
31400
1.240
1-26495
1.438
I-459S7 I
389 I
41132 I
339 I
36214 I
289 I
3 130 1
1.239
1.26397
1-437
1-45853 I
388 I
41033 I
338 I
36116 I
288 I
31203
1.238
1.26299
1.436
1-45759 I
387 I
40935 I
337 I
36017 I
287 I
31x06
1.237
1.26201
1-435
1.45661 I
386 I
40837 I
336 I
35919 I
286 1
31008
1-236
1. 26103
1-434
1-45563 I
385 I
40738 I
335 I
35820 I
28s I
30909
1-235
1. 2 6005
1-433
1.45464 I
384 I
40640 I
334 I
35722 I
284 1
30811
1-234
1-25907
1.432
1.45366 I
383 I
40541 I
333 I
35624 1
283 1
30713
1-233
1.25809
1.43 1
1.45267 I
382 I
40443 I
332 I
35526 1
282 1
3061S
1-232
1.25711
381 I
40345 I
331 I
35428 I
281 1
30517
I-231
1.25613
DIAMETERS OF FORMING TOOLS
259
Table 4. — For Finding Diameters of Circular Forming
Tools for Brown & Sharpe No. 2 Automatic "
Screw Machine
No. 2
No. 2
No. 2
No. 2
No. 2
Base
Line
Radius
Base
Line
Radius
Base
Line
Radius
Base
Line
Radius
Base
Line
Radius
1.230
1-25515
1.178
1.20424
1.126
1.15342
1.074
1. 10271
1.022
1-05213
1.229
I. 25417
1. 177
1.20326
1.125
1.15244
1.073
1.10174
1.021
1.05116
1.228
1-25319
1.176
1.20228
1.124
1-15147
1.072
1.10076
1.020
1-05019
1.227
I. 25221
1-175
1.20130
1.123
1.15049
1.071
1.09979
1.019
1.04920
1.226
I. 25123
1.174
1.20032
1.122
1.14951
1.070
1.09882
1.018
1.04825
1. 225
1.25025
I-I73
1.19934
1. 121
1-14854
1.069
1.09784
1.017
1.04728
1.224
1.24927
1.172
1.19837
1.120
1.14756
1.068
1.09687
1.016
1.04631
1.223
1.24829
1. 171
I-I9739
1.119
1.14659
1.067
1.09590
1.015
I-04S33
1.222
I. 24731
1.170
1.19641
1.118
1.14561
1.066
1.09492
1.014
1.04436
1. 221
1-24633
1.169
I-19543
1.117
1.14463
1.065
1-09395
1.013
1-04339
1.220
1-24535
1.168
1.19446
1.116
1.14366
1.064
1.09298
1.012
1.04242
1. 219
1-24437
1.167
I-19348
1-115
1.14268
1.063
1.09200
1.011
1.0414S
1. 218
1-24339
1.166
1.19250
1.114
1. 14171
1.062
1.09103
l.OIO
1.04048
1. 217
1. 24241
1.165
1.19152
1.113
1.14073
1.061
1.09006
1.009
1.03951
I.216
1. 24143
1.164
1.19054
1.112
1.13976
1.060
1.08908
1.008
1-03854
1. 215
1.2404s
1.163
1. 18957
1.111
1.13878
1.059
1.08811
1.007
1-03757
I.2I4
1-23947
1.162
1.18859
I.IIO
1.13780
1-058
1.08714
1.006
1.03660
1. 213
1.23849
1.161
1.18761
1.109
1-13683
1-057
1.08616
1-005
1-03563
1. 212
1-23752
1.160
1.18663
1.108
1.13586
1.056
1.08519
1.004
1.03466
1. 211
1-23654
I-159
1.18566
1. 107
1.13488
I 055
1.08422
1.003
1-03369
1. 210
1-23556
1-158
1. 18468
1.106
1. 13390
1.054
1.08324
1.002
1-03273
1.209
1-23458
I-157
1-18370
1.105
1-13293
I-053
1.08227
l.OOI
1-03175
1.208
1.23360
1-156
1. 18272
1.104
1-13195
1.052
1.08130
1.000
1.03078
1.207
1.23262
I-155
I-18175
1.103
1.13098
1.051
1.08032
•999
1.02981
1.206
1. 23164
1-154
1.18077
1.102
1.13000
1.050
1.07935
.998
1.02884
1.205
1.23066
I-153
1.17979
1.101
1.12903
1.049
1.07838
.997
1.02787
1.204
1.22968
1.152
1.17881
1. 100
1.12805
1.048
1.07741
.996
1.02690
1.203
1.22870
1.151
1.17784
1.099
1.12708
1.047
1.07643
.995
102593
1.202
1.22772
1.150
1.17686
1.098
1.12610
1.046
1.07546
•994
1.02496
1. 201
1.22675
1.149
1.17588
1.097
1. 12513
1.045
1.07449
.993
1-02399
1.200
1.22577
1.148
1.17491
1.096
1-1241S
1.044
1-07352
.992
1.02302
1. 199
1.22479
1.147
I-17393
1.095
1.12318
1.043
1.07254
.991
1.02205
1. 198
I.22381
1.146
1.17295
1.094
1.12220
1.042
1.07157
.990
1.02108
1. 197
1.22283
I-I45
1-17197
1.093
1. 12123
1.041
1.07060
.989
1.02011
1. 196
1. 22185
1.144
1.17100
1.092
1.12025
1.040
1.06963
.988
1. 01914
I-I95
1.22087
I -143
1.17002
1.091
1.11928
1.039
1.06865
.987
1.01817
1.194
1. 21989
1.142
1.16904
1.090
1.11830
1.038
1.06768
.986
1.01720
I-I93
1.21891
1.141
1.16807
1.089
1-11733
1.037
1.06671
.985
1.01623
1. 192
1. 21793
1.140
1.16709
1.088
1-11635
1.036
1.06574
•984
1.01526
1. 191
1. 21696
I-I39
I. 16612
1.087
1-11538
1035
1.06477
•983
1.01429
1. 190
1. 21598
I-138
1.16514
1.086
1.11440
1.034
1.06379
.982
1.01332
1. 189
1. 21500
I-137
1.16416
1-085
1-11343
1-033
1.06282
.981
1.01235
1. 188
1. 21402
1-136
1.16318
1.084
1.11246
1.032
1.06185
.980
1.01139
1. 187
1. 21304
I-135
1.16221
1.083
1.1114S
1.031
1.06088
•979
1.01042
1. 186
1. 21206
I-134
1.16123
1.082
1.11051
1.030
1.05991
-978
1.00945
1. 185
1.21108
I-133
1.16025
1.081
1-10953
1.029
105893
-977
1.00848
1. 184
1.21011
I-132
1.15928
1.080
1.10856
1.028
1.05796
-976
1.00751
I.183
I. 20913
I-131
1-15830
1.079
1.10758
1.027
1-05699
•975
1.00654
1. 182
I. 20815
1-130
I-15732
1.078
1.10661
1.026
1.05602
.974
1-00557
I.181
I. 20717
1.129
I-15635
1.077
1.10563
1-025
1-05505
•973
1.00460
1. 180
I. 20619
1.128
I-I5537
1.076
1.10466
1.024
1.05408
.972
1.00363
1. 179
I. 20521
1. 127
1.15440
I.07S
1.10369
1.023
1.05310
.971
.970
1.00267
1.00170
26o SCREW MACHINE TOOLS, SPEEDS AND FEEDS
HARDENING SPRING COLLETS AND FEED CHUCKS
Before hardening collets it is common practice to open them some-
what to insure their having a given tension after hardening and
tempering so that they will open and release the stock the instant
they are themselves freed by the chucking mechanism. This opening
of the chuck must be carefully attended to or an eccentric and un-
satisfactory job will result. Sometimes a simple fLxture having a cone
pointed spindle is used for this purpose, the collet being held centrally
while the cone plunger is forced between the chuck jaws to open them
evenly the necessary amount. No matter how much care is taken in
this operation, the effect is lost unless the hardening is properly at-
tended to and only grinding will produce a perfectly true collet.
Preventing Distortion. — Some toolmakers take the precaution of
leaving a thin fin of metal at the front end of the collet in each saw
slot as at ^ , Fig. 1 5, in order that when hardened there shall be no chance
of distortion due to un-
equal springing of the
jaws. This metal tie or
bridge at the ends of the
jaws is removed by grind-
ing out with a thin slitting
wheel or lap. Another
method, shown at B, also
leaves a narrow ring at
the front end to run on
grinder center while collet
is ground outside. The
^^^- ^5 ring at the end of the nose
may be ground off leaving the collet ready for use.
Another method of preventing trouble in hardening is to inserta
piece of metal, say 3V inch thicker than the width of the saw slot, in
the front end of the slots and then wire the nose of the chuck tightly
so as to retain the steel pieces during the hardening process. The
collet must be heated uniformly and dipped so as to insure all three
prongs being cooled simultaneously. With the best of care a coUet
that is hardened but not ground afterward will generally require
touching up on the conical portion of one or two of the prongs to insure
its running true. It is not difficult, however, to make the coUet run
true within 0.002 inch by polishing one or two prongs.
In order that the collet may close parallel it must be fairly long and
the outside of each prong or jaw may be relieved by filing so as to
insure its bearing along the center line on the conical surface. It
must be carefully tempered at the ends of slots to prevent breaking.
Feed Chucks. — Feed chucks need no such refinement in their
production. Thej^ are usually closed after slitting on opposite sides
so that after hardening they will maintain a constant grip on the
stock sufficient to feed it forward when it is released by the chuck.
The idea is indicated at C, Fig. 15. Ordinarily the hole for the stock
should be bored a little over size otherwise the corners of the feed
chuck jaws when drawn back over the stock will mar the surface.
CUTTING SPEEDS AND FEEDS
261
Cm
8
1
-it
1^1
fg'giiirr
IM
10 Ov ro M 0\ t^\0 0
0) M M M
ill
OOiOiOioOOO
r°l
Oh
5
u
w
u
IM
"^ uoO r-- r^ r^ r^oo
8 8 8 8 8 8 8 8
IM
0 0 0 M <N TfOO VO
0 <N00 CMOM ONi>.
10 Tt (N M M M
^11
^~»l
«|00 rHlTJ COH< -hH* r^b^ «|-*
Oh
5
g
2
i
-0 MOO 0 OoOt^Os
M M LOOO M VO <N 0
00 Tj- CS N M H M
^11
0 0 OiotoioO 0
^^1
rHHCdOOHN"!-* ^ '^'J^"'^
Oh
s
u
w
gfisirii
> u e
lOO 0^ rooO to Os (^
tJ-C^vO m 100 WOO
(N M M
00000000
00 f^ t^ i>.o ^o ^ 0
H«imJ^r-iHK«|<»HMm|-« ^ "^
*J
<
S
P>j
U
m
>4
i^.
Hi
0
to
^
1
w
T)
f^
Q
>-<
;?
<
<D
rn
Q
>^
W
i
m
,n
0
.=1
^
S!
[ij
J3
p
(3
u
tn
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<N
D.
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h-l
^
H
X
S^,
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Oh
w
z
1^^
mvotn
Cj rO M <N '^00 T}- r^.
OOtOLotoOOO
6^1
„,^^.M^,«N^H.-*.
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q q q q q 0 0 0
000 invo <N •^00
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t4
1
262 SCREW MACHINE TOOLS, SPEEDS AND FEEDS
SPEEDS AND FEEDS FOR SCREW MACHINE WORK
The accompanying tables of speeds and feeds for different types
of tools used on materials commonly worked in the automatic screw-
machine have been compiled from data accumulated and thoroughly
tested during extended experience in this class of work.
It is, of course, impossible, where a series of tools is used on an
automatic machine, to select speeds theoretically correct for every
tool carried by the turret and cross slide. A compromise is necessary
and therefore speeds are selected which will fall within the range
suitable for the different tools.
Speeds and Feeds for Turning
Tables i and 2, page 261, cover turning speeds and feeds for bright-
drawn stock (screw stock) and brass, with various depths of chip (that
is, stock removed on a side) from 3^ up to J inch. These feeds and
speeds and depths of cut are figured more especially for such tools
Table 3. Speeds and Feeds for Finish Box Tool
Screw Stock
Brass Rod
-^fc-ii
c^U
^ <u 0
Feet
Rev.
Feed
Feet
Rev.
Feed
EQo
Surface
per
per
Surface
per
per
<'Sog
Speed
Min.
Rev.
Speed
Min.
Rev.
*
80
2445
.0045
180
5500
.0045
.0025
tV
70
1426
.0055
180
3668
•0055
.0025
i
6^
993
.0075
180
2750
.0075
.0045
^
60
458
.oil
180
1375
.011
.006
1
60
305
.012
180
917
.012
.006
I
60
229
.012
175
668
,012
.0065
I^
55
140
.014
170
433
.014
.007
2
50
95
.014
170
325
.014
.008
With high speed steel tools the above speeds may be increased about 30 per cent
and feeds 10 to 20 per cent.
as roughing boxes where the cut, though frequently heavy, is taken
by a single cutting tool. For a xVi^ich chip the feeds for various
diameters of stock are practically midway between those tabulated
for J-and J-inch chips. The feed per revolution for f chip taken on
diameters ij inch and larger is the same as given for \ inch chip,
the speed also being the same for corresponding diameters. Where
hollow mills are used on steel and the work is divided among three
or more cutting edges the feed per revolution for a given depth of
chip is about 25 per cent coarser than given for box tools; with both
classes of tools the feeds are, of course increased as the diameter of
FEEDS FOR FORMING TOOLS
263
the stock increases, the peripheral speeds being reduced as the feeds
grow coarser. The speeds and feeds for finishing box tools as used
on screw stock and brass are given in Table 3, the last column indi-
cating the amount of stock which, generally speaking, it is advisable
to remove in order to produce a good surface.
Forming-tool Speeds and Feeds
Speeds and feeds for forming tools are given in Tables 4 and 5.
It will be seen that after a work diameter of about J inch has been
reached, a tool about |-inch wide is adapted to take the coarsest
feed, tools from this width up to approximately j\ (such as com-
monly employed for cutting-off purposes) admitting of heavier
crowding as a rule than either the narrower or wider tools.
Table 4. Speeds for Forming
1
Screw Stock
Brass Rod
1
Screw Stock
Brass Rod
Feet
Surface
Speed
Rev.
per
Ivlin.
Feet
Surface
Speed
Rev.
per
Alin.
Feet
Surface
Speed
Rev.
per
Min.
Feet
Surface
Speed
Rev.
per
Min.
t
f
75
75
70
65
2292
1528
1069
662
200
200
185
185
6112
4074
2827
1885
f
f
I
60
60
60
60
360
305
229
153
^7S.
175
175
170
1050
882
667
432
i
^5
497
185
1414
2
50
96
170
324
With high speed steel tools the above speeds n
lay be increased a
bout 30 per cent.
Table 5. Feeds for F
ORMiNG Tools
Width
Smallest Diai!
[ETER OF Form
of
Form
z\
1
JS
1
1
i
f
i4
tV
.0007
.0008
.001
.0012
-.0012
.0012
.0012 •
.0012
i
.0005
.0008
.001
.OG12
.0015
.0020
.0025
.0025
i
.0007
.001
.001
.0015
.0015
.0018
.0018
f
.0009
.001
.001
.0012
.0015
.0015
^
.0008
.0009
.001
.001
.0015
.0015
!
.0008
.0009
.001
.0011
.0012
I
.0008
.0009
.001
.0012
i^
.0007
.0007
.0009
.0011
2
.0007
.001
With cutting-ofiF tools of high speed steel the above feeds may be increased 10 U
20 per cent.
204 SCREW MACHINE TOOLS, SPEEDS AND FEEDS
Drilling Speeds and Feeds
Drilling speeds and feeds are given in Table 6. While these
speeds are based on much higher peripheral velocities than drilU
makers as a rule recommend for general purposes, it should be
noted that conditions for drilling in the automatic, on the ordi-
nary run of work, are usually ideal so far as lubrication, steadi-
ness of feed, etc., are concerned, and it is possible where the holes
drilled are comparatively shallow and the drill has ample oppor-
tunity for cooling during operation of the other tools, to maintain
speeds that would be considered too high to be attempted in general
shop practice.
Table 6. Drilling Feeds and Speeds
With* high speed drills the above speeds may be increased about 30 per cent.
Speeds and Feeds for Reaming
Table 7 is made up of speed and feed data for reamers. In
this table the feed for different classes of material has been consid-
ered as constant for any given diameter of reamer, although it is
probable that with certain materials, especially on brass alloys, etc..
the feed per revolution might be increased somewhat, to advantage,
over the rates given. These feeds have been tabulated, however, as
representing highly satisfactory practice in reaming the materials
listed.
THREADING, COUNTERBORING, ETC. 265
Table 7, Reaming Feeds and Speeds
u
Rev. per Min.
^
Rev. per Min.
B
Feed
Amount
to
Feed
Amount
to
a
V
CA
per
Remove
Screw
Brass
t4
per
Remove
Screw
Brass
0
Rev.
on
Stock
Rod
0
Rev.
on
Stock
Rod
a
Dia.
at
at
rt
Dia.
at
at
P
40 Ft.
130 Ft.
Q
40 Ft.
1 30 Ft.
^
.005
.0045
1222
3972
li
.018
.010
122
397
t\
.006
.0045
815
2648
I*
.020
.010
102
331
i
.007
.006
611
1986
If
.022
.010
87
284
i
.0085
.006
407
1324
2
.024
.013
76
248
i
.0105
.008
306
993
2i
.026
.013
68
220
t
.012
.008
245
795
2j
.028
.013
61
199
i
.014
.008
204
662
2|
.030
.013
56
181
I
.016
.010
153
497
3
.032
.013
51
165
With high speed reamers the above speeds may be increased about 20 per cent
Threading, Counterboring, Etc.
Table 8 explains itself and, while giving speeds for threading work
with dies, should be of equal value in establishing speeds for tapping.
Table 8. Speeds for Dies. Standard Threads
WITH high-speed STEEL DIES
Screw Stock
Brass Rod
Si
Screw
Stock
Brass Rod
h
H
0
Feet
Rev.
Feet
Rev.
-K
Feet
Rev.
Feet
Rev.
rt
Surface
per
Surface
per
ci
Surface
per
Surface
per
Q
Speed
Min.
Speed
Min.
5
Speed
Min.
Speed
Min.
i
40
1222
135
4126
f
35
178
115
586
i
40
611
125
1909
I
30
115
no
420
i
35
35^
120
1222
li
30
92
100
306
i
35
267
120
917
i^
30
76
90
229
t
35
210
120
715
2
25
48
85
162
For carbon steel dies run at 50 to 75 % of above speeds.
For feeds for counterbores from f inch to 2 inches diameter,
Tables i and 2 for turning may be followed where the counterbores
cut to a depth from one half to three quarters their diameter. Where
cutting deeper than about one diameter, the feeds should be decreased;
in such depths it is well to withdraw the counterbore during the
cutting operation to free it from chips.
PUNCH PRESS TOOLS
METHOD OF FINDING THE DIAMETERS OF SHELL
BLANKS
This method for the finding of diameters of shell blanks, applies
also to some other shapes which frequently occur in practice.
The method is based upon the surface of the shell in comparison
with the area of the blank and should therefore be used only when
light material is to be considered. In case of the flanged shapes the
width of the flange should be small in proportion to the diameter.
Cylindrical Shell
Fig. I shows a cylindrical shell of the diameter d and the depth //.
To find the diameter of the blank, lay down the diameter d of the
shell twice on a horizontal line, Fig. 2, add to this a distance equal
to four times the depth h of the shell and describe a semicircle of
which the total distance is the diameter. The vertical Une D from
the intersecting point with the circle to the horizontal line gives the
desired blank diameter. Line D is to be drawn at a distance d from
the end of the horizontal.
Flanged Shells
If the shell has a flange as in Fig. 3, add four times the width of
this flange to the horizontal line and proceed as above ; see Fig. 4.
In the case of a hemisphere, Fig. 5, lay down the diameter three
times on the horizontal hne and draw the vertical line at the dis-
tance d from the end, as in Fig. 6.
If the hemisphere has a flange as in Fig. 7, add a distance equal
to twice the width of the flange to the horizontal line, as in Fig. 8.
In any case, the length of the vertical line D gives the desired diam-
eter of blank.
Taper Shells
If a shell with tapering sides, Fig. 9, has to be drawn, multiply
first the bottom diameter by itself and divide the product by the
sum of the two diameters di and d in order to obtain the length x.
Otherwise proceed as shown in Fig. 10.
Flanged Taper Shells
If the taper shell has a flange of the width a, Fig. 11, add to the
base line of the diagram twice this width, as shown in Fig. 12.
266
DIAMETERS OF SHELL BLANKS
267
1 o
^ —
T
II
^ 0
Q
^ 6
-Q— >
-p
4)
.L
"T
rN^
^
j^
• _i.
J
b
c
JS
X"
5
1
_
(U
1
rC
C]^ 00
C/3
»+-l
0
0
> ta
12
' r
4J
•
^
?
S
.■i_
Cj.
tfe,
43 d
268 PUNCH PRESS TOOLS
TABLE OF DIAMETERS OF SHELL BLANKS
The table shows the diameters of blanks for shells i x j inch to
6x6 inches inclusive, by j inches. The figures were obtained by
the formula given on page 267:
D = Vc?( d-\- 4 h)
where,
d = Diameter of finished shell.
h = Hight of finished shell.
They were also checked by figuring on the area of the metal.
If it is desired to punch the metal in one or more operations,
get the mean hight of the shell by the following formula;
ht
where T
m = Mean hight of finished shell.
h = Hight of finished shell.
t = Thickness of finished shell.
T = Thickness of metal before drawing.
Suppose for example, a shell 2 inches diameter by 6 inches high;
thickness of metal before drawing, 0.040 inch; finish thickness of
shell, 0.020 inch. Then
h t 6 X 0.020 . 7
7n = — = = 3 inches.
T 0.040
By using this hight, from the table we find a shell 2 inches diameter
by 3 inches high requires a blank 5.29 inches diameter.
When the shell has rounded corners at the bottom, subtract the
radius of the corner from the figures given in the table. Thus, in
Fig. 13
the last example, suppose the shell to have a radius of | inch on
the corner; 5.29 — 0.125 = 5.165 inches, the required diameter
of the blanks.
When a shell has a cross-section similar to the ones shown in
Fig. 13, the required blank diameter may be calculated by the fol-
lowing formula:
where
' W t
d = Diameter of blank in inches;
W = Weight of shell;
^ = Weight of one cubic inch of the metal;
t = Thickness of shell.
DIAMETERS OF SHELL BLANKS 269
Diameter of Blanks for Shells, j x j Inch to 6 x 6 Inches
=: a
Right of Shell
i"
i"
S."
i"
li"
A"
il"
2"
2\"
2\"
21"
3"
,.
0.56
0.75
0.90
E
1.03
1.14
1.25
1.35
1.44
I.S2
1.60
1.68
1-75
¥'
0.87
1. 12
1-32
1.50
1.66
1.80
1.94
2.06
2.18
2.2Q
2.40
2.50
¥
1. 14
1.44
1.68
1.89
2.08
2.25
2.41
2.5b
2.70
2.84
2.97
3.09
1"
1.41
1-73
2.00
2.24
2.45
2.65
2.83
3.00
3.I6
3-32
3.40
3.61
li"
i.b8
2.01
2.30
2.56
2.79
3.01
3-21
3.40
3.58
3.75
3-91
4.07
I-"
1.94
2.29
2.60
2.87
3-12
3.3b
3-57
3.78
3-97
4.15
4.33
4.50
II"
2.19
2.50
2.88
3-17
3-44
3-08
3.91
4-13
4.34
4-53
4.72
4.91
2'
2-45
2.83
3-16
3.46
3-74
4.00
4.24
4-47
4.69
4.90
5.IO
5-29
2-"
2.70
3.09
3-44
3-75
4.04
4.31
4-56
4.80
5.03
5.25
5.46
5.66
2-"
2-"
2.96
3-30
3-71
4-03
4-33
4.61
4.«7
5-12
5.36
5.50
5.81
6.02
3.21
3.01
3.Q8
4-31
4.62
4.91
5.18
5.44
5.68
5-92
6.1S
6.37
3"
3-4(>
3.87
4.24
4..S8
4.90
5.20
5.48
5.74
6.00
6.25
6.48
6.71
3-"
3-71
413
4-51
4-«5
5.1H
5.4H
5.77
6.04
6.31
6.56
6.80
7.04
3-
3-97
4-39
4-77
5-12
5-45
5-77
6.06
6.34
6.61
6.87
7.12
7.36
3-"
4.22
4.b4
5 -03
5-39
5-73
6.05
6.35
6.64
6.91
7.18
7.44
7.69
4 „
4-47
4.90
5-29
5.66
6.00
6.32
6.63
6.93
7.21
7.4«
7.75
8.00
4i"
4.72
5-15
5-55
S-92
b.27
b.6o
6.91
7.22
7.50
7.78
8.05
8.31
4^
4-9«
5-41
5.81
6.19
0.54
6.87
7-10
7.50
7-79
8.08
8.35
8.62
4r
5.22
5-00
6.07
6-45
6.80
7.15
7-47
7.78
8.08
8.37
8.65
8.92
5'
S.4«
5-92
6-32
6.71
7.07
7.42
7.75
8.06
8.37
8.66
8.94
9.22
5*
S.73
6.17
6.58
6.97
7-33
7.68
8.02
8.34
8.65
8.95
9.24
9-52
5"!
5.Q«
b.42
6.84
7-23
7.60
7.95
8.29
8.62
8.93
9.23
9-53
9.81
if
6.23
6.68
7.09
7.49
7.86
8.22
8.56
8.89
9.21
9-52
9.81
10.10
6"
t).4H
6.93
7-35
7-75
8.12
«.49
8.83
9.17
9-49
9.80
10.10
10.39
Hight of SheU
3i"
31"
3l"
4"
41"
4¥'
4f"
5"
Si"
5l"
51"
6"
1"
1.82
1.89
1.95
2.01
2.08
2.14
2.19
2.25
2.30
2.36
2.41
2.46
5"
2.60
2.69
2.78
2.87
2.96
3.04
3.12
3.21
3.29
3.3b
3.44
3, SO
f"
3.21
3.33
3.44
3.54
3.b5
3.75
3.85
3.95
4.04
4.13
4.22
4.31
l'
3-74
3.87
4.00
4.12
4.24
4.30
4.47
4.58
4.69
4.80
4.90
5.00
1?"
4.22
4.37
4-51
4.64
4.77
4.91
5.03
5.15
5.27
5.39
5.50
5.02
I-"
4.66
4.82
4.98
5.12
5-27
5.41
5-55
5.08
5.81
5.94
6.06
6.18
I-"
5.08
5.26
5.41
5.58
5.73
5.88
6.03
6.17
6.31
6.45
6.58
6.71
2"
5.48
5.66
5.83
6.00
6.16
6.32
6.48
6.63
6.78
6.93
7.07
7.21
2r
5.86
6.05
6.23
6.41
6.58
6.75
6.91
7.07
7.23
7.39
7.54
7.69
2 k"
6.22
6.42
6.61
6.80
6.98
7.16
7.33
7.50
7.66
7.82
7.98
8.14
2i"
6.58
6.79
6.99
7.18
7-37
7.55
7.73
7.91
8.08
8.25
8.41
8.58
3"
6.93
7.14
7-35
7-55
7-75
7.94
8.12
8.31
8.49
8.66
8.83
9.00
3i"
7.27
7.49
7.70
7.91
8. II
8.31
8.50
8.69
8.88
9.06
9.24
9.41
4
7.60
7.83
8.0s
8.26
8.47
8.67
8.87
9.07
9.26
9.45
9.63
9.81
3i"
7.92
8.16
8.38
8.61
8.82
9.03
9.24
9-44
9.63
9.83
10.02
10.20
4"
8.25
8.49
8.72
8.94
9.17
9.38
9-59
9.80
10.00
10.20
10.39
10. s8
4i"
8.56
8.81
9.04
9.28
9.50
9.72
9.94
10.15
10.36
10.56
10.76
10.96
44"
8.87
9.12
9.37
9.60
9.84
10.06
10.28
10.50
10.71
10.92
II. 12
11.32
4f
9.18
9.44
9.69
9-93
10.16
10.40
10.62
10.84
11.06
11.27
11.48
11.69
5"
9.49
9.75
10.00
10.25
10.49
10.72
10.95
II. 18
11.40
11.62
11.83
12.04
5 k"
9-79
lo.os
10.31
10.56
10.81
11.05
11.28
II. 51
11.74
11.96
12.18
12.39
^K
10.08
10.36
10.62
10.87
II. 12
11.37
II. 61
11.84
12.07
12.30
12.52
12.74
5i"
10.38
10.66
10.92
ri.i8
11.44
11.69
11-93
12.17
12.40
12.63
12.85
13.08
b"
10.68
10.9s
11.23
11.49
11.75
12.00
12.25
12.49
12.73
12.96
13.19
13.42
270
PUNCH PRESS TOOLS
PUNCH AND DIE ALLOWANCE FOR ACCURATE
WORK
In the blanking, perforating and forming of flat stock in the power
press for parts of adding machines, tj-pewriters, etc., it is generally-
desired to make two different kinds of cuts with the dies used. First,
to leave the outside of the blank of a semi-smooth finish, with sharp
corners, free from burrs, and with the least amount of rounding on
the cutting side. Second, to leave the holes and slots that are per-
Punch
Fig. 14. — Blanking Tools
Punch
Fig. 15. — Perforating Tools
forated in the parts as smooth and straight as possible, and true to
size. The table given is the result of considerable experimenting
on this class of work, and has stood the test of years of use since it
'was compiled.
The die always governs the size of the work passing thi^ough it.
The punch governs the size of the w^ork that it passes through. In
blanking work the die is made to the size of the work wanted and
the punch smaller. In perforating work the punch is made to the
size of the work wanted and the die larger than the punch. The
clearance between the die and punch governs the results obtained.
CLEARANCE FOR PUNCHES AND DIES
271
Figs. 14 and 15 show the application of the table in determining
the clearance for blanking or perforating hard rolled steel .060 inch
thick. The clearance given in the table for this thickness of metal
is .0042, and Fig. 14 shows that for blanking to exactly i inch diam-
eter this amount is deducted from the diameter of the punch, while
for perforating the same amount is added, as in Fig. 15, to the diameter
of the die. For a sliding fit make punch and die .00025 to .0005 inch
larger; and for a driving fit make punch and die .0005 to .0015 inch
smaller.
Table of Allowances for Punch and Die for Different
Thickness and Materials
Thickness of Stock
Inch
Clearance for Brass
Clearance for Medi-
Clearance for Hard
and Soft Steel
um Rolled Steel
Rolled Steel
Inch
Inch
Inch
.010
.0005
.0006
.0007
.020
.001
.0012
.0014
.030
.0015
.0018
.0021
.040
.002
.0024
.0028
.050
.0025
.003
•0035
.060
.003
.0036
.0042
.070
•0035
.0042
.0049
.080
.004
.0048
.0056
.090
.0045
.0054
.0063
.100
.005
.006
.007
.110
•0055
.0066
.0077
.120
.006
.0072
.0084
.130
.0065
.0078
.0091
.140
.007
.0084
.0098
.150
.0075
.009
.0105
.160
.008
.0096
.0112
.170
.0085
.0102
.0119
.180
.009
.0108
.0126
.190
.0095
.0114
•0133
.200
.010
.012
.014
CLEARANCE FOR PUNCHES AND DIES FOR
BOILER WORK
The practice of the Baldwin Locomotive Works on sizes up to ij
inches is to make the punch -^^ inch below nominal size and the die
eV inch above size, which gives gV inch clearance. Above ij inches
the punches are made to nominal size and the dies 3V inch large, which
allows the same clearance as before. The taper on dies below ij
inches is i inch in 1 2 ; on sizes above i-
inch in 12 inches.
272 PUNCH PRESS TOOLS
LUBRICANT FOR PRESS TOOLS
Although there are some shops in which no lubricant is used
when working sheet metal, and where good results are obtained, still
it is best to use a lubricant on all classes of sheet-metal work.
For all cutting dies on brass and steel a heavy animal oil is best.
Pure lard oil is very satisfactory, although expensive.
When punching copper, or German silver, a thin coating of lard
oil or sperm oil should be spread over the sheets or strips before
punching. A good way to do this evenly is to coat one sheet thickly
and then feed it through a pair of rolls, after which a number of other
sheets may be run through the rolls and thus coated evenly. For
drawn work this method of coating the sheets from which the shells
are to be drawn will be found to be the best, as the coating of oil on
the stock will be very thin and it will not be found necessary to clean
the shells afterward, the oil having disappeared during the blanking
and drawing process. When oil is applied with a pad or brush the
coating will be so thick that it will be necessary to clean the article
produced.
Drawing Steel Shells
In drawing steel shells a mixture of equal parts of oil and black
lead is very useful, and while it may be used warm it does not affect
the work as much as the speed of the drawing press does; the thicker
the stock the slower must be the speed of the punch. A heavy
grease with a small proportion of white lead mixed in with it is also
recommended for this purpose.
If the drawing die is very smooth and hard at the corner of the
"draw," or edge of the die, the liability of clogging will be reduced
to a minimum. Often it will help to give to the die a lateral polish
by taking a strip of emer}^ cloth and changing the grain of the polish
from circular to the same direction as the drawing.
Lubricants for Brass
For drawing brass or copper a clean soap water is considered most
satisfactory. One of the largest brass firms in this country uses a
preparation made by putting 15 pounds of Fuller's soap in a barrel
of hot water, and boiling until all the lumps are dissolved. This
is used as hot as possible. If the work is allowed to lie in the
water until a slime has formed on the shell it will draw all the
better. A soap that is strong in resin or potash will not give
good results.
In drawing zinc the water should be hot, or the percentage of broken
shells wiU be large.
Aluminum is an easy metal to draw, but it hardens up very
quickly. For lubricants lard oil, melted Russian tallow and vasel-
ine are all good. The lubricant should be applied to both sides
of the metal.
BROACHES AND BROACHING
Broaching is being used more and more to finish holes and even
for slots and the outside of pieces of work. In most cases it is used
to change a round hole to a square or other shape, such as the four
or ten key ways used in automobile transmission.
The chip cut by each tooth varies from o.ooi to 0.007 inch, accord-
ing to the material being cut and the accuracy required. The teeth
are usually undercut from 6 to 10 degrees to give a curl to the chip,
while the top clearance is about 30 degrees. Some EngUsh practice
The First Chip
The Last Chip
Fig. I
Section of Broached Hole
undercuts 25 degrees, having top nearly flat. The distance between
teeth varies according to the length of the hole being broached, the
spacing being larger for long holes so as not to have too many teeth
engaged at once, three being a good number. Spacing varies with
length of hole.
In broaching square holes from the round, or in other cases where
there is a decided change of shape, the first teeth take the widest
cut as at vl. Fig. i. This evens up the work of the different teeth
Fig. 2
as to the length of surface cut as the hole approaches a square as
seen at B.
The blank for the cutting part of each broach is first turned taper
by an^mount equal to the total cut of the teeth. The tooth spaces
are then turned | inch apart and about ^2 i^^ch deep, this depending
on the diameter of the broach, as it must not be unduly weakened;
it is then milled ^| inch square as shown. The longer the hole the
more chip room must be provided.
273
274
BROACHES AND BROACHING
Where the hole or other surface to be broached is short, the teeth
are often cut on an angle to give a shearing cut. This is also done
to prevent chatter at times, another remedy being to space the teeth
unevenly as with reamers.
The solid broach is used more than any other. But as tool steel
is apt to spring in hardening, and to break out teeth at times, some
use built-up or sectional broaches, espe-
cially on large work where the solid
broach costs heaxaly. Some use low
carbon steel, case hardened. These
sectional broaches are made in a variety
of ways. Figs. 2 to 4 showing a few
examples. In Fig. 2 sections are set in
on the side, while in Figs. 3 and 4 the
sections are practically disks held on a
central arbor. In some cases seyeral
teeth are made on one section. Fig. 4 is made in the same way for
broaching internal gears having 66 teeth, 20 diametral pitch and ^
inch face. Each tooth cuts 0.006, the last three teeth being straight
to insure the size being accurate.
Fig.
Fig. 4
BROACHING ROUND HOLES
Round holes have been broached instead of reamed in some places
for many years and the practice is growing. It was formerly con-
fined to soft metal, such as shaft bearings, but is now being made
to cover all the metals, in some few cases broaching from a cored
hole. For small work a small arbor press \\ith a sort of sub-press
can be used to advantage. For larger work the arbor press operated
by power is very good and of course the regular broaching machine
can be used in any case.
Two broaches used in one shop are shown in Fig. 5, other sizes
can be made in proportion. These were used in a hand arbor press.
The first 5 or 6 teeth do most of the cutting as these broaches only
finish the holes instead of reaming. In some cases with broaches for
soft metal bearings and even in cast iron, the large end is left plain
and a trifling amount larger than the last tooth. It then acts as a
burnisher and compresses the metal. This requires a large amount
of power. •
In broaching round holes in cast iron, the broach was made from
0.0002 to 0.0003 i^ch larger than the nominal size and the land was
0.012 as shown. The holes were drilled close to size so as to leave
very little work for the broach. In this case about 0.002 inch was
left for broaching.
BROACHING SQUARE HOLES
275
The comparison between broaching and reaming in this case is
interesting. The reamers would wear appreciably below size in 25
holes while one broach finished 5000 holes to size.
i.
-3V,6
S^Vie-
m.
14 Broach
-0-012
I liiii
-2-%-
'1^
"
%
'T
[|
iii
i
IH" Broach
B SS;
TO SAVE TIME IN BROACHING OUT SQUARE HOLES
The fit of the gears on a square shaft depends almost entirely
on the flat surfaces at or near the corners. With this in mind, it is an
econom}' to bore or drill the round hole in the gear slightly larger than
the diameter across the flats of the squared shaft, as shown in Fig. 6.
Taking a ij-inch
square shaft and bor-
ing the hole x\ inch
larger or ly^ inches in
diameter, we see in
the illustration exact-
ly what this would
mean. The amount
of metal to be cut out
would be materially
reduced, the portion
A to B not being
touched by the broach
in any way. Yet the
remaining surface in
the corners would be ample to carry all the load of the gears at work,
and the clearance A to B would allow the best of lubrication.
The center relief, as shown, gives considerable added chip space as
well as reduces the amount of chip, thus allowing a heavier chip per
tooth. This may either reduce the length of the broach or allow a
longer hole (such as two gears at once) to be broached with the same
length of broach.
The set of 7 broaches shown in Fig. 7 show the practice of the
Brown & Sharpe Mfg. Co. in making automobile transmission gears.
The gears are of a tough alloy steel making the 7 necessary to secure
an accurate hole of ij inches across the flats. Each broach is 30I
inches long, the cutting portion being only 17^ inches. The method
of holding the shank can be readily seen.
''''///////^^///////MV////^A
Fig. 6
276
BROACHES AND BROACHING
S 1.5745
§ 1.5745
-%5745
is |§
1.357 1.313 1.280 1.258
1.3595 1.315 1.2815 1.259
1.362 1.317 1.283 1.260
1.3645 1.319 1.2845 1.261
1.367 1.321 1.286 1.262
1.3695 1.323 1.2875 1.263
1.372 1.325 1.289 1.264
1.3745 1,327 1.2905 1.265
1.377 1.329 1.292 1.266
1.3795 1.331 1.2935 1.267
1.382 1.333 1.295 1.268
1.3845 1.335 1.2965 1.269
■=J 1.387 1.337 1.298 1.270
1.3895 1.339 1.2995 1.271
1.392 1.341 1.301 1.272
1.3945 1.343 1.3025 1.273
1.397 1.345 1.304 1.274
1.3995 1.347 1.3055 1.275
1.402 1.349 1.307 1.276
1.4045 1.351 1.3085 1.277
I 1.407 1.353 1.310 1.278
1.4095 1.355 1.3115 1.279
1.412 1.357 1.313 .1.280
^718^
&
^w^ Fig. 7
SIX-SPLINE FITTINGS
277
6 Spline Fittings
Permanent Fit
To blide vben not
Under Load
I
To BUde when Under
Load
6-Spline Fittings for Automobiles
From sixth Report of Broaches Division S.A.E. Accepted at
Meeting of Society, January, 1914
C .
D
d
w
T
D
d
w
T
D
d
w
T
za
• 750
.„
.188
80
•750
.638
.188
•750
.600
.188
•749
.674
.187
•749
.637
.187
.749
.599
.187
152
.875
.788
.219
109
.875
•744
.219
•875
.700
.219
.874
.787
.218
•874
•743
.218
159
•874
•699
.218
207
1. 000
■999
.900
.899
.250
.249
143
1. 000
•999
•850
.849
.250
.249
208
1. 000
•999
.800
•799
-250
•249
270
1. 125
I.013
.281
■80
I-I2S
•956
.281
263
I^I25
.900
.281
1.124.
1.012
.280
1.124
1-955
.280
i.i^
•899
.280
342
1.250
1.249
I-125
1. 124
-313
-312
.«
1.250
1.249
1:063
1.062
•313
•312
325
1.250
1.249
1. 000
•999
•313
•312
421
1-375
1-374
1.238
1-237
•344
-343
269
1-375
1-374
1. 169
1. 168
•344
•343
393
I-37S
1-374
1. 100
1.099
•344
-343
510
1.500
I-3SO
•375
321
1-500
1-275
•375
468
1.500
1.200
-375
608
1-499
1-349
-374
1.499
1.274
•374
1.499
1. 199
-374
1.625
1.463
.40b
376
1.625
I-381
.406
1
1.625
1.300
.406
1.624
1.462
■405
1.624
1.380
•405
550,
1.624
• 1.299
-405
713
I-750
I-57S
.438
436
1-750
1.488
-438
637
1-750
1.400
-438
827
1.749
1-574
•437
1.749
1.487
-437
1.749
1-399
-437
2.000
1.800
.500
S70
2.000
1.700
.500
833;
2.000
1.600
.500
1080
1.998
1.798
-498
1.998
1.698
-498
1.098
1.598
•498
2\
2.250
2.025
-S63
721
2.250
I^9i3
-56^
2.250
1.800
-56s
1367
2.248
2.023
-561
2.248
1.912
-561
2.248
1-708
.S6i
2?
2.500
2.250
-625
891
2.500
2.125
.625
2.500
2.000
.625
1688
2.49«
2.248
-623
2.498
2.123
-623
2.498
1.998
-623
3
3.000
2.700
-750
1283:
3.000
2-550
• 750
1873
3.000
2.400
-750
2.99«
2.698
-74«
2.998
2-548
.748
2.998
2.398
-748
2430
T = 1000 X 6 (No. of Splines) X Mean Radius X /s X i = inch-pounds torque
capacity per inch bearing length at 1000 lbs. pressure per square inch on sides of
splines. No allowance is made for radii on comers nor for clearances.
278
BROACHES AND BROACHING
10 Spline J'ittings
To Slide when not
Under Load
To Blide vhen Under
io-Spline Fittings for Automobiles
From Sixth Report of Broaches Division S.x^.E. Accepted at
Meeting of Society, January, 19 14
1 .
6 §
D
d
w
T
D
'd
• w
T
D
d'
w
T
!z;q
3
•750
.683
.117
120
•750
-645
•117
.83
.750
.608
.117
241
•749
.682
.116
•749
.644
.116
•749
.607
.116
.«75
-796
.137
165
•875
•753
• 137
248
•875
•709
-137
329
.874
•795
.136
•874
•752
• 136
•874
.708
.136
1. 000
.910
.1S6
,.'
1. 000
.860
.156
326
1. 000
.810
.156
•999
.909
-155
•999
•859
• 155
•999
.80Q
•155
430
t1
1. 125
1.024
.176
271
1. 125
.968
.176
4I2|
I^I25
.911
.176
545
1. 124
1.023
•175
1. 124
■967
•175
1. 124
.910
•175
tI
I.2SO
1-138
•195
336
1-250
1^075
•195
508
1.250
1.013
• 195
672
1.249
I-137
.194
1.249
1.074
1. 183
.194
1.249
1.012
.194
jI
1-375
1. 251
•215
406,
1-375
• 215
6m'
i^375
1. 114
• 215
813
1-374
1.250
.214
1-374
1. 182
.214
i^374
1. 113
.214
li
1.500
1-365
•234
483
1.500
1.290
•234
732
1.500
1-215
• 234
967
1.499
1-364
•233
1.499
1.289
•233
1.499
1. 214
•233
I 5
I-t.2S
1.479
•254
566
1.62s
1.398
■ 254
860
1.625
1.316
• 254
"35
1.624
1.478
•253
1.624
i^397
•253
1.624
I-315
• 253
I?
1-750
1-593
•273
658
I-750
1-505
• 273
997
I-750
1.418
• 273
1316
1.749
1-592
.272
1.749
1-504
.272
1.749
1.417
.272
2.000
1.820
1.818
.ST2
860
2.000
1.720
.^12
2.000
1.620
.M2
1.998
.310
1.998
1.718
.310
1.998
1.618
.310
2\
2.250
2.048
•351
1088
2.250
i^935
•351
1647
2.250
1-823
•351
2176
2.248
2.046
•349
2.248
i^933
•349
2.248
1.821
•349
2i
2.500
2.275
•390
1343
2.500
2.150
•390
2034
2.500
2.025
•390
2688
2.498
2.273
•388
2.498
2.148
.388
2.498
2.023
•388
3.000
2.730
.468
3.000
2.580
.468
3.000
2.430
.468
3869
2.998
2.728
.466
2.998
2-578
.466
1
2.998
2.428
.466
T = 1000 X 10 (No. of Splines) X Mean Radius X h X 1 = inch-pounds torque
capacity per inch bearing length at 1000 lbs. pressure per square inch on sides of
.Splines. No allowance is made for radii on corners nor for clearances.
BOLTS, NUTS AND SCREWS
U. S. STANDARD BOLTS AND NUTS
The U. S. Standard for bolts, nuts, etc., called also Sellers' Stand-
ard, Franklin Institute Standard, and American Standard, was recom-
mended in 1864 by the Franklin Institute for general adoption by
engineers. (See Note).
Strength of U.
S. Standard
Bolts
FROM
I TO
3^^ Diameter
Bolt
Areas
Tensile Strength
Shearing
Strength
^
!
-S
n
I
H.
a
Full Bolt
Bottom of Thread
t^
^
*«
i
a
r,
-^
^a
M
i^
i^
1
L
1
0
s
0 ^
h
y
u
l^
U
.2
h5"
S
3
0
fi
:^
:^
fs.
!^
TH.
a
0
Z
fa
03
<
<
<
<
<:
<
<
I
20
.049
.027
270
340
470
380
490
200
270
"16
18
.077
•045
450
570
790
580
770
340
450
f
16
.110
.068
.680
850
1,190
830
1,100
510
680
t\
14
.150
•093
930
1,170
1,630
1,130
1,500
700
930
i
13
.196
.126
1,260
1,570
2,200
1,470
1,960
940
1,260
1%
12
.248
.162
1,620
2,030
2,840
1,860
2,480
1,220
1,620
f
II
•307
.202
2,020
2,520
3,530
2,300
3,070
1,510
2,020
1
10
.442
.302
3,020
3,770
5 ,290
3,310
4,420
2,270
3,020
1
9
.601
.419
4,190
5,240
7,340
4,510
6,010
3,150
4,190
I
8
.785
•551
5,510
6,890
9,640
5,890
7,850
4,T3o
5,510
ll
7
•994
.693
6,930
8,660
12,130
7,450
9,940
5,200
6,930
li
7
1.227
.890
8,890
11,120
15,570
9,200
12,270
6,670
8,900
'f
6
1.485
1.054
10,540
13,180
18,450
11,140
14,850
7,910
10,540
li
6
1.767
1.294
12,940
16,170
22,640
13,250
17,670
9,700
12,940
if
5i
2.074
1-515
15,150
18,940
26,510
15,550
20,740
11,360
15,150
if
5
2.405
1.745
17,450
21,800
30,520
18,040
24,050
13,080
17,440
ll
5
2.761
2.040
20,490
2=;, 610
^v5,86o
20,710
27,610
15,370
20,490
2
4i
.142
2.300
23,000
28,750
40,250
23,560
31,420
17,250
23,000
2?
4i
3-976
3.021
30,210
37,770
^2,870
29,820
39,760
22,660
30,210
2j
4
4.909
3.716
37,160
46,450
65 ,040
36,820
49,090
27,870
37,160
2f
4
5 -940
4.620
46,200
57,750
80,840
44,580
59,400
34,650
46,200
3
3i
7.069 5.428
54,280
67,8:;o
94.990
53.020
70,69c
40,710
54,280
Note. — The distance between parallel sides of the bolt head and nut for a rough
bolt is one and one-half diameters of the bolt plus one-eighth of an inch. The thickness
of the head in this system for a rough bolt is equal to one-half the distance between its
parallel sides. The thickness of the nut is equal to the diameter of the bolt. It
was originally recommended in this system that the thickness of the head for a
finished bolt be equal to the thickness of the nut, and that the distance between the
parallel sides of a bolt head and nut and the thickness of the nut be one-sixteenth
mch less for finished parts than for rough. However, it is the practice of bolt and
nut manufacturers to make finished U. S. nuts to the same dimensions as established
for rough ones, and where finished heads are required to the U. S. Standard they are
customarily made to the same dimensions as rough heads unless otherwise specified.
279
28o
BOLTS, NUTS AND SCREWS
5>Q
Roug-h
Heads and Kuts
.A X 1.155. C=A X 1.414
U. S. Standard Bolts and Nuts
ROUGH
Dia. of
Threads
per Inch
Across
Flats
Across Corners
Thickness
Depth of
Bolt
B
C
Head
Nut
Thread
1
4
20
h
H
If
1
i
•0325
A
i8
M
ii
H
• H
tV
.0361
f
i6
H
li
fi
H
1
.0406
t\
14
If
ft
i/i
If
tV
.0464
h
13
1
i.\
li ■
i\
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.0500
T%
12
U
li
If '
H
t\
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1
ir
iiV
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li
H
1
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f
10
li
Iff
Iff
f
f
.0650
i
Q
iTff
41
23\
11
I
.0722
I
8
If
li
2if
if
.0812
li
7
III
2^\
2t\
If
Ij
.0928
1?
7
2
2A
2M
I
li
.0928
l|
6
2tV
2H
3iV
I3V
If
.1083
li
6
2i
2f
3li
iiV
li
.1083
If
5
2f
3fV
3ll
li
^4i
.1300
2
4i
3i
3tl
4||
ii\
2
.1444
2i
4j
3i
4o%
4M
If
2i
.1444
2i
4
3i
4li
sH
III
2i
.1625
2|
4
4i
4tl
^eh
2|
2f
.1625
3
3i
4l
5M
6H
2r%
3
•1857
Note. — U. S. Government Standard Bolts and Nuts are made to
above U. S. or Sellers' Standard Rough Dimensions. The sizes of
finished bolt heads and nuts are the same as the sizes of the rough
ones, that is for finished work the forgings must be larger than for
rough, thus the same wrench may be used on both black and finished
heads and nuts.
XJ. S. STANDARD BOLTS AND NUTS
281
Finished
JHeads and Nuts
w\
m
See Note
U. S. Standard Bolts and Nuts. — finished heads and nuts
FINISHED heads AND NUTS
See Note
i
"o
V
N
1
Q
a
h
3
"0
."2
-a
Safe Strain in lbs.
Iron at 50,000
lbs. per Sq. In.
Factor of Safety
5
i5
<
g
c
0
U
i
1
i
tV
i
t\
.185
.191
.0063
.0260
260
i\
H
If
i
.2408
.246
.0069
.0452
452
1
f
II
tV
.2938
if
.0078
.0677
677
7
II
If
i
•3447
If
.0089
.0932
932
h
if
if
tV
.4001
il
.0096
•1257
1257
9
If
leV
§
•4542
M
.0104
.1620
1620
•f
I
l3\
T%
.5069
If
.0114
.2018
. 2018
f
lA
i|i
U
.6201
f
.0124
.3020
3020
1
If
iM
If
•7307
tl
.0139
.4194
4194
T
lT6
ill
H
.8376
II
.0156
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5509
li
If
.2^1
itV
•9394
U
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6930
li
iH
2M
It\
1.0644
1/5
.0179
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8890
If
2|
2ll
lA
^•i585
iH
.0208
1.054
10540
li
2^
41
ixV
1-2835
iM
.0208
1-293
12930
If
2H
3a\
IH
1 .4902
Iff
.0250
1.744
17440
2
3j\
3H
lil
1.7113
III
.0278
2^3
23000
2i
3tV
3fi
2-h
1-9613
iH
.0278
3.021
30210
2i
3il
4M
2tV
2.1752
2tV
•0313
3-714
37140
2f
4t\
4tl
2^
2.4252
2tV
•0313
4.618
46180
3 ■
4A
53\
2i|
2.6288
2tf
•0357
5-427
54270
282
BOLTS, NUTS AND SCREWS
[I
d
^
V
lllllr
\
/
_JI
1
I
N
)
u
^
Machine Bolts with Manufacturers Std
Heads
1
Hex', and Square Heads
(National Machinery Co.)
Hex. and Square Nuts
a
-a
i
J
.c^
V
et^
^
I
2i
f5
E2J
5|
S 3
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Bz
ua
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o
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s d
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6
13 oo
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2k
iffi
o cr
•,H^
Q
^
<
<
H
<
<:
<
H
1
3
7
3
"?
1
5
3
4
«
tV
16
To
2
8
16
A
i8
it
H
1
4
H
ft
1
i
f
i6
ft
f
A
1
2 3
32
57
04
-h
T^^
14
M
ft
u
If
ft
I
f
h
13
3
4
il
1
if
if
1/2
t\
t\
12
II
ft
11
II
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1
5
8
II
H
I
H
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T%
1
lO
li
it\
A
it\
Ifi
iM
W
1
9
IT^^
If
H
If
iM
lit
if
8
l|
lA
3
4
it\
lit
2ii
if
li
7
lii
If
II
lit
23%
2^
l|
li
7
l|
III
if
2
2^
2ff
t1
If
6
2tV
2i
lA
2A
2M
33%
If
I^
6
2i
2A
li
2f
2f
3lf
I^
If
5l
2tV
2|
I/.
2A
2ii
3l
if
If
5
2f
2H
ir\
2f
3A
3fl
l|
l|
5
2H
2|
iM
2H
3ii
Ah
l|
2
4l
3
3tV
i|
3i
3ff
4fl
2
Note. — Nuts supplied by different makers for manufacturers
standard bolts vary somewhat as regards thickness. The above
nut sizes are Hoopes and Townsend Standard.
SET SCREWS
283
c^ — , Cone Point and " ™ , „, ^ „ • x
^^^ Hanger Set Point 0, Flat Pivot Point
^^_^ c5 >;* §
IOia.=lBot. ofThd.
/»^6fl^
Set Screws
Hartford Machine Screw Co. Standard
1
2:
-0
a
U
2
■-3
1
1
.bib
D
L
H
Hi
c
M
R
F
N
I
1
1
f
i ■
I
20
18
16
14
13
12
II
10
9
•8
1
f
7
8
I
M
If
1
i
1
1
M
.A
t¥8
If
li
If
i
i
h
1
i
I
.019
.021
.023
.027
.031
.032
.034
•037
.041
.047
.075
.083
.094
.107
.125
•125
.130
.150
.166
.187
284
BOLTS, NUTS AND SCREWS
E^""^
Hartford Machine Screw Co., Standard
Hexagon Head Cai
Screws
Square Head Cap Screws
.
.
-d
^
..
ri
Id
da
Is
11
0
<
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ll
3
1
Is
la
<
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s
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Q
Q
H
p;;
Q
P
H
rt
D
A
1
B
C
R
A
B
c
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1
4
20
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1
4
3
4
il
1
1
IS
i8
37
1
55
5
•7
5
15
IT
61
2
16
64
8
16
16
16
1
i6
u
A
t
H
M
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f
itV
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14
II
t
tV
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h
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1
3
4
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1/2
M
5
8
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it
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lit
M
ii
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III
1
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f
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1
10
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3
4
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7
8
I
III
1
9
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li
1
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li
7
8
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I
8
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li
I
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III
l|
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2||
li
7
iH
If
li
2f
lit
If
li
3
li
7
4i
i^
li
2M
2\
li
li
3t^
FILLISTER HEAD CAP SCREWS
^S^''"'T3
:r+^
285
□
Collar Head Screws
Fillister Head Cap Screws
(P. & .W. St'd)
.3
0
1
h
<
ii
15
Q
<
1^
1
C
0
to
y
C
73
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-a
X
i
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1
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0
'0
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0
a
Q
Q
D
A
B
C
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F
R
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c
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c +
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3^2
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i
40
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1%
32
it
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1
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1
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.165
i
1
286
BOLTS, NUTS AND SCREWS
u m^~^
Flat, Round and Oval Fillister Head Cap Screws
^
^^
"rt
^
a^^
d"^
1
t3
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^ 0
1
:3
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c
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R
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L
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BUTTON AND COUNTERSUNK HEAD CAP SCREWS 287
Button Head Cap Screws
Flat
4.NB Oval Countersunk Head
Cap Screws
T3
-d
^
T3
ll
-0
1
1
0
,1
"0
2
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288
BOLTS. NUTS AND SCREWS
k-'^Zga
Machine Screws. American Screw Company
Flat Head
Round Head
No.
A
B
C
E
F
B
C
E
F
2
.0842
.1631
•0454
.030
.0151
•1544
.0672
.030
.0403
3
.0973
.1894
•0530
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.0177
.1786
.0746
.032
.0448
4
.1105
.2158
,0605
•034
.0202
.2028
.0820
.034
.0492
5
.1236
.2421
.0681
.036
.0227
.2270
.0894
.036
•0536
6
.1368
.2684
•0757
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.0252
.2512
.0968
•039
.0580
7
.1500
.2947
.0832
.041
.0277
•2754
.1042
.041
.0625
8
.1631
.3210
.0908
.043
•0303
.2996
.1116
•043
.0670
9
.1763
•3474
.0984
•045
.0328
.3238
.1190
.045
.0714
lO
.1894
•3737
.1059
.048
•0353
•3480
.1264
.048
.0758
12
.2158
.4263
.1210
.052
.0403
.3922
.1412
.052
.0847
14
.2421
.4790
.1362
•057
•0454
.4364
.1560
•057
.0936
i6
.2684
•5316
•1513
.061
.0504
.4806
.1708
.061
.1024
i8
.2947
.5842
.1665
.066
•0555
.5248
.1856
.066
.1114
20
.3210
.6368
.1816
.070
.0605
.5690
.2004
.070
.1202
22
•3474
•6895
.1967
•075
.0656
.6106
.2152
•075
.1291
24
•3737
.7421
.2118
.079
.0706
.6522
.2300
.079
.1380
26
.4000
.7421
.1967
.084
.0656
.6938
2448
.084
.1469
28
.4263
.7948
.2118
.088
.0706
•7354
.2596
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•1558
30
.4526
.8474
.2270
•093
•0757
.7770
•2744
•093
.1646
Dimensions given are maximum, the necessary working varia-
tions being below them.
FILLISTER HEAD MACHINE SCREWS
289
U>^<22>i
Machine Screws. xA.merican Screw Company
Fillister Head
No.
A
1
G
B
C
D
E
F
2
0842
•1350
•0549
.0126
.030
.0338
.0675
.3
0973
.1561
.0634
.0146
.032
.0390
.0780
4
1105
.1772
.0720
.0166
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•0443
.0886
5
1236
.1984
.0806
.0186
.036
.0496
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6
1368
.2195
.0892
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.1097
7
1500
.2406
.0978
.0225
.041
.0602
.1203 •
8
1 63 1
.2617
.1063
.0245
.043
.0654
.1308
9
1763
.2828
.1149
.0265
•045
.0707
.1414
10
1894
.3040
•1235
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.048
.0760
.1520
12
2158
.3462
.1407
.0324
.052
.0866
•1731
14
2421
.3884
.1578
.0364
•057
.0971
.1942
16
2684
•4307
•1750
.0403
.061
.1077
•2153
18
2947
.4729
.1921
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.1182
.2364
20
3210
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.0483
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.1288
.2576
22
3474
•5574
.2267
.0520
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.1384
.2787
24
3737
•5996
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.1499
.2998
26
4000
.6419
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.0601
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.1605
.3209
28
4263
.6841
.2779
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30
4526
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•3632
290 BOLTS, NUTS AND SCREWS
American Screw Company. Standard Threads per Inch
No.
2
3
4
5
6
7
8
9 10
12
Threads
per Inch
48
64
48
56
32,36
40
30
32
36
30
32
30
36
24, 30,
32
20
24
No.
14
16
18
20
22
24
26
28
30
Threads per
Inch
18
20,
24
16,18,
20
16,18
14
16
18
14,16
A.S.M.E. STANDARD PROPORTIONS OF MACHINE SCREWS
The diagram and tables herewith show the proportions of machine
screws as recommended by the committee of the American Society
of Mechanical Engineers on Standard Proportions for Machine
Screws, the report of this committee being adopted by the Society
at its spring meeting, 1907.
The included angle is 60 degrees, and the flat at top and bottom
of thread is one eighth of the pitch for the basic or standard diam-
eter. There is a uniform increment of 0.013 inch, between all sizes
from 0.06 to 0.19 (numbers o to 10 in the tables which follow) and
of 0.026 inch in the remaining sizes. This change has been made
in the interest of simplicity and because the resulting pitch diameters
are more nearly in accord with the pitch diameters of screws in pres-
ent use.
• The pitches are a function of the diameter as expressed by the
formula >-
Threads per inch = =- — -^ ,
^ D -\- 0.02
with the results given approximately, so as to avoid the use of frac-
tional threads.
The diagram shows the various sizes for both 16 and 72 threads
per inch, and shows, among other things, the allowable difference in
the flat surface, between the maximum tap and the minimum screw,
this variation being from one-eighth to one sixteenth.
The minimum tap conforms to the basic standard in all respects,
except diameter. The difference between the minimum tap and
the maximum screw provides an allowance for error in pitch and
for wear of tap in service.
The form of tap thread shown is recommended as being stronger
and more servictable than the so-called V-thread, but as some
believe a strict adherence to the form shown might add to the cost of
small taps, they have decided that taps having the correct angle
and pitch diameter are permissible even with the V-thread. This
will allow a large proportion of the taps now in stock to be utilized.
The tables given by the committee were combined into the present
compact form by the Corbin Screw Corporation.
A. S. M. E. MACHINE SCREW DIAGRAM
291
ri'^fi
292
BOLTS, NUTS AND SCREWS
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TAPS FOR A. S. M. E. STANDARD SCREWS 293
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296
BOLTS. NUTS AND SCREWS
PROPORTIONS OF MACHINE SCREW HEADS
A. S. M. E. Standard
The four standard heads are given herewith. These proportions
are based on and include the diameter of the screw, diameter of the
head, thickness of head, width and depth of slot, radius for round
and fillister heads, and included angle of the flat-head screw.
Oval Fillister Head Machine Screws. A. S. M. E. Standard
OVAL fillister HEAD SCREWS
A = Diameter of Body.
B = 1.64^ — .009 = Diam. of Head and
Rad. for Oval
C = 0.66^ — .002 = Hight of Side
V = .173^ + .015
^ = li? = Depth of Slot
F = .134B + C = Hight of Head.
-^D^
^-
-n,rTs;
— f -
m.i. /
! ^
4t
—
-- ►
A
B
C
D
E
F
.060
.0894
.0376
.025
.025
.0496
'<^1Z
.1107
.0461
.028
.030
.0609
.086
.132
.0548
.030
.036
.0725
.099
•153
.0633
.032
.042
.0838
,112
•1747
.0719
•034
.048
•0953
.125
.196
.0805
'^Z1
•053
.1068
.138
.217
.089
•039
•059
.1180
•151
.2386
.0976
.041
.065
.1296
.164
•2599
.1062
.043
.071
.1410
.177
.2813
.1148
.046
.076
.1524
.190
.3026
.1234
.048
.082
.1639
.216
•3452
.1405
.052
•093
.1868
.242
.3879
.1577
-'^^l
.105
.2097
.268
•4305
.1748
.061
.116
•2325
.294
•4731
.192
.066
.128
•2554
.320
.5158
.2092
.070
.140
.2783
.346
.5584
.2263
•075
.150
.3011
•372
.601
•2435
.079
.162
.3240
.398
•6437
.2606
.084
•173
.3469
.424
.6863
.2778
.088
.185
.3698
.450
.727
•295
•093
.201
.4024
FLAT FILLISTER HEAD MACHINE SCREWS 297
Flat Fillister Head Machine Screws. A. S. M, E. Standard
FLAT FILLISTER HEAD SCREWS
A = Diameter of Body
B = 1. 64 A — .009 = Diam. of Head,
C = 0.66A — .002 = Hight of Head
D = 0.173^ + .015 = Width of Slot
E = ^C = Depth of Slot
-B ^
I — HD;-
bZUT
I
^.-4a->
A
B
C
D
E
.060
.0894
.0376
.025
.019
.073
.1107
.0461
.028
.023
.086
.132
.0548
.030
.027
.099
.153
.0633
.032
.032
.112
.1747
.0719
•034
.036
.125
.196
.0805
•037
.040
.138
.217
.0890
•039
.044
•151
.2386
.0976
.041
.049
.164
•2599
.1062
.043
.053
.177
.2813
.1148
.046
•057
.190
.3026
.1234
.048
.062
.216
•3452
.1405
.052
.070
.242
.3879
•1577
•057
.079
.268
•4305
.1748
.061
.087
.294
•4731
.1920
.066
.096
.320
.5158
.2092
.070
.104
.346
•5584
.2263
•075
.113
•372
.601
•2435
.079
.122
•398
•6437
.2606
.084
.130
424
.6863
.2778
.088
.139
.450
•727
•29s
•093
.147
298 BOLTS. NUTS AND SCREWS
Flat Head Machine Screws. A. S. M. E. Standard
FLAT HEAD SCREWS
A = Diameter of Body
B = 2A — .008 = Diam. of Head
C = ■ ~ '°° = Depth of Head
1.739
D = .173^ + .015 = Width of Slot
E = IC = Depth of Slot
.J2-Deg.-
^^
iV
\
-^t'rr
\'
^
/{
, A-—
A
B
c
D
1
E
.060
,112
1
.029
.025
I ^10
•073
.138
j '^21
.028
1 .012
.086
.164
.045
.030
1 .015
.099
.190
.052
.032
.017
.112
.216
.060
.034
' .020
.125
.242
.067
«o37
, .022
.138
.262
.075
•039
.025
•151
.294
.082
.041
.027
.164
.320
.090
.043
.030
.177
.346
.097
.046
.032
.190
•372
.105
.048
'03S
.216
.424
.120
.052
.040
.242
.472
•135
•057
.045
.268
.528
.150
.061
.050
.294
.580
.164
.066
.055
.320
.632
.179
.070
.060
.346
.682
.194
'OlS
.065
.372
:732
.209
.079
.070
•398
.788
.224
.084
.075
.424
.840
•239
.088
.080
450
.892
.254
•093
.085
ROUND HEAD MACHINE SCREWS 299
Round Head Machine Screws. A. S. M. E, Standard
ROUND HEAD SCREWS
A — Diameter of Body
B = i.S^A — .005 = Diam. of Head
C = .yA = Hight of Head
D = .173^ + .015 = Width of Slot
£ = JC + .01 = Depth of Slot
A
B
c
D
!
E
.060
.106
.042
.025
.031
.073'
.130
.051
.028
•035
.086
•154
.060
.030
.040
.099
.178
.069
.032
.044
.112
.202
.078
.034
.049
.125
.226
.087
•037
•053
.138
.250
.096
•039
.058
•151
.274
.105
.041
.062
.164
.298
.114
.043
.067
.177
.322
.123
.046
.071
.190
.346
•^33
.048
.076 •
.216
•394
•151
.052
.085
.242
.443
.169
•057
.094
.268
.491
.187
.061
.103
.294
•539
.205
.066
.112
.320
•587
.224
.070
.122
.346
.635
.242
•075
•131
.372
.683
.260
.079
.140
.398
•731
.278
.084
.149
.424
•779
.296
.088
.158
•450
.827
•315
•093
.167
300
BOLTS, NUTS AND SCREWS
Hot Pressed and Cold Punched Nuts
U. S. Standard Hot Pressed and
Cold Punched Nuts
Cold Punched Check and
[am Nuts
HEXAGON AND SQUARE
HEXAGON
Dia.
Across
Thick-
Dia.
Dia.
Across
Thick-
Dia.
Bolt
Flats
ness
Hole
Bolt
Flats
ness
Hole
1
.
1
4
^
\
1
tV
if
T^
if
t\
i
if
7
■32
i
f
16
f
9
f
H
H
f^
11
tV
-i
tV
fl
A
il
h
1
h
il
h
A
M
A
M
T%
If
tV
fi
M
If
•L
itV
f
f 1
f
ItV
If
1
li
f
1
li
tV
1
1
ItV
i
a
I
ItV
i
11
If
H
If
tV
H
li
III
li
if
ll
iH
1
if
2
ItV
li
2
f
ItV
if
2t\
lA
if
2tV
V
I/^
jl
2|
l|
lA
li
2i
13%
If
2t%
If
iM
If
2tV
If
III
if
2|
If
li
if
2f
I
ll
l|
2M
l|
If
ij
2l|
irV
if
2
3l
2
Iff
2
31
li
Iff
2l
3T6
4
lit
H
3l
2i
iM
2|
3H
2|
2tV
2*
3i
2i
2ii
21
4i
2f
2||
3
4l
3
2f
Finished case-hardened and semi-finished nuts are made to the
above dimensions. Semi-finished nuts are tapped and faced true
on the bottom.
HOT PRESSED NUTS
301
Hot Pressed Nuts
Hot Pressed Nuts, Manufacturers
Hot Pressed and Forged Nuts. Manufac-
Standard
turers Standard
HEXAGON
Square
Dia.
Across
Thick-
Dia.
Dia.
Across
Thick-
Dia.
Bolt
Flats
ness
Hole
Bolt
Flats
ness
Hole
i
f
i
3^
i
1
i
s\
t\
A
-,%
F
1
T%
■i^
f
f
1
H
f
f
ih
T^
1
tV
II
tV
1
7
T^
If
h
I
i
tV
i
^
i
tV
F
i|
9
T6
I
t\
li
t\
1
f
I4
f
^
1
li
1
f
if
u
f
I*
f
II
1
Is
1
li
1
If
i
II
I
^4
I
i
I
2
I
i
ij
2
li
li
ll
24
Ij
II
I?
2i
If
l3\
Ij
2J
li
l3\
if
22
li
lA
if
2f
if
it\
i|
2|
if
it\
I*
3
I|
Il%
i|
3
if
itV
If
3i
I|
IT%
If
3i
l|
It\
if
3i
If
IT^
li
3^
2
IH
li
3f
l|
ill
2
3i
2
III
2
4
2
I If
2j
3f
21-
ll
2g-
4
2i
l|
2i
3f
21
2
2?
4i
2i
2
2i
4
2|
2j
2| .
4i
2i
2i
22
4i •
2^
2i
2^
4i
2i
2-1
2|
42
2f
2t^^
2f
4f
2f
2-(T.
3,
4f
3
2-i
3
5
3
2-6
3i
5
3i
2-|
3i
5i
3i
2-6
3§
5i
3i
3h
32
6
3i
3i
302
BOLTS, NUTS AND SCREWS
Cold Punched Nuts, Manufacturers Standard
Hexagon
Square
Dia.
Across
Thick-
Dia.
Dia.
Across
Thick-
Dia.
Bolt
Flats
ness
Hole
Bolt
Flats
ness
Hole
\
f
i
^2
i
J
i
#
l\
1%
T%
f
A
1
1
1
j'
f
3
4
f
M
1^6
1
T5
13
f.
1
^
M
1
1
^
i
i
tV
i
I
1
t\
1
i
tV
i
I
A
T6
A
l|
p-
i
li
t\
i
1
l|
A
F
li
1
T^
f
f
A
1
Ii
1
♦
1
M
1
li
f
f
If
f
H
1
if
|1
1
1.
If
1
if
1
f^
1
if
7
■ ■
I*
1
^1
1
if
1
If
y
l|
^
2 1
¥2
If
i:
•■
I*
i
1*
2
i
1
4
I
25
Ij
2
Is
1 5
T6
1
If
1
II
l|
2i
l|
M
1
if
ft
If
2l
Ii
ItV
If
2^
^4
itV
If
Ij
1
if
2f
if
IT%
li
2
Ii
\l
I^
3
li
^¥
If
2i
If
lT^6
if
3i
If
'<^
2i
li
If^
If
3*
if
It\
4
2f
i|
IT%
. li
3f
l|
iH
If
3
If
II'.
2
4
2
iH
3i
i|
il^e-
ii
3i
2
li^
2
3i
2
lyl
2
3l
2i
III
HOT PRESSED NUTS
303
Hot Pressed Nuts. Manufacturers Standard Narrow Gage Sizes
Dimensions of Whitworth Standard Hexagonal Nuts and Bolt-Heads
Dia.
of
Bolt
Width of X
Nut or Bolt ^
Head across pi
Flats ^°^
ligbt
of
t Head
Dia.
of
Bolt
Width of
Nut or Bolt
Head across
Flats
Hight
of
Bolt Head
i
.338
109
li
2.048
1.094
^^®
•448
164
if
2.215
1.203
i
•525
219
i^
2.413
1.312
A
.601
273
if
2.576
1.422
1
.709
328
if
2.758
I-53I
V-
.820
383
If
3-018
1. 641
h
.919
437
2
3149
I-750
1%
I. on
492
2|
3-337
1-859
f
I.IOI
547
2i
3-546
1.969
H
1. 201
601
25
3-750
2.078
1. 301
656
2i
3-894
2.187
U
1.390
711
2-
4-049
2.297
I
1.479
766
2f
4.181
2.406
it
I-S74
820
2S
4-346
2.516
1
1.670
87s
3
4-531
2.625
i|
1.860
984
304
BOLTS, NUTS AND SCREWS
Button Head Machine and Loom Bolts
HOOPES & TOWNSEI^ Co.
Diameter Bolt. .
t\
1
4
A
f
tV
h
fk
.
•3.
1
I
Diameter Head .
4
t
H
i^
itV
I^
ifV
if
if
l|
2k
Thickness of
Head
s\
1
/i
t\
i
1
4
A
f
h
f
f
Carriage Bolts
Upson Nut Co.
Diameter Bolt. .
t\
1
4
^
f
%
i
A
f
1
f
I
Diameter Head .
t\
f*^
H
H
ItV
ItV
lA
ir'e
iH
2t\
Thickness of
Head
A
i
i-.
-1%
s\
1
4
3\
/.
'
t\
^
LENGTHS OF BOLTS
Square Head, Hexagon Head, Button Head, Round Head and
Cone Head bolts are measured under the head. Countersunk
Head bolts, bolt ends and rods are measured over all.
Lengths of Threads Cut on Bolts
Length of Bol
ts i & A
!&/.
l&i%
1
f
1
I
li
li
I to iV
.. f
1
li
if to 2 "
8
I
li
li
if
2|tO 2i"
I
li
li
If
If
2f to 3 "
I
li
I?
I4
2
2i
3l to 4 "
li
J^4
li
li
if
2
2i
2i
4i to 8 "
li
li
I?
2
^1
2f
3.
81 to 12 "
li
I^
If
2
2i
3.
■4
12^ to 20 "
i^
2
2
2
2i
3
3i
3i
Bolts longer than 20 inches and larger than ij inch in diameter
are usually threaded about 3 times the diameter of the rod.
MACHINE AND TAP BOLTS
305
Round and Square Countersunk Head Bolts
Diameter Bolt
Diameter Round Head ....
Distance across Flats Square
Head
Thickness Square and
Round Heads
i
It
¥
ft
4
1
1
h
if
H
ft
1
11
13^
li
ii^
A
t\
-h
i
i
3%
A
H
M
Tap Bolts
Diameter Bolt
No. of Threads per Inch . . .
Across Flats Hex. and Square
Heads
Across Comers Hex. Head .
Across Comers Square Head
Thickness Hex. and Square
Heads
i
T^^
f
t\
i
T%
f
f
1
20
18
16
14
13
12
II
10
9
f
M
A
U
f
n
H
li
lA
T^
T2
3
4
n
M
I.v
Hf
iM
i-i
U
H
it
II^
ItV
Ili
iH
4f
A
i
A
1
tV
§
H
1
f
li
2i
Stove Bolt Diameters and Threads
(^
Dia. of Bolt
No. of Threads per Inch ,
i
-,%
A
aV
i
tV
32
28
24
22
18
18
3o6
BOLTS, NUTS AND SCREWS
Eefers to all Nuts
and Screw Heads,
d =Dia. Cotter Pin
Hr
t— a-*
K-H-i
DX 1.5 Length of Thread
P^Pitch of Thread
-|-=Flat
All heads and nuts to be semi-finished. All screws to be of steel
not less than 100,000 pounds tensile strength and 60,000 pounds
elastic limit per square inch. Screws, screw heads and plain nuts
to be left soft. Castle nuts to be case-hardened. Where screws
are to be used in soft material such as cast iron, brass, bronze or
aluminum, the U. S. S. pitches are to be used. Body diameter to
be o.ooi inch less than nominal diameter with a plus tolerance of
zero and a minus tolerance of 0.002 inch. Nuts shall fit without
perceptible shake. This was originally known as the A. L. A. M.
Standard, but is now the S. A. E. (Society Automobile Engineers).
Automobile Screw
AND
Nut Stand
\RDS Adopted by the S.
A. E.
D
i
A
f
A
h
9
T6
f
ii
1
7
8
I
P
28
24
24
20
20
18
18
16
16
14
14
A
z%
M
if
II
T%
n
If
fl
if
If
I
a
/^
U
u
f
tV
u
If
if
B
If
1
B
tV
h
T%
1
f
1
8
if
I
ItV
li
ItV
C
A
j\
i
1
8
t\
t\
\
i
i
1
4
1
4
E
5
6?
-i^
1
^
i
z\
h
A
A
A
3^^
H
t\
if
j%
u
1
II
if
If
T^e
If
3
4
I
^
^V
i
i
i
\
1
i
i
i
i
K
IV
t\
A
A
A
3^-
3\
A
A
3\
3^
d
-h
tV
aV
-i-2
A
i
i
i
i
i
i
L
t
if
A
V.
f
H
H
lA
li
It\
i^
BOLTS AND NUTS
Planer Nuts
307
Diameter of Bolt
No. of Threads per Inch
Across Flats
Thickness
h
f
1
i
I
i|-
11
II
10
0
8
7
I
ItV
li
^i\
If
III
{'i
I
I J
itV
lA
If
li
7
2
2t^^
Coupling Bolts
^CJ
n
Diameter of Bolt
No. of Threads per Inch
Short Diameter of Head
Length of Head
Thickness of Nut
Short Diameter of Nut .
i
f
f
I
I
a
^-^
II
10
Q
8
7
1
ItV
li
itV
i|
1^1
h
t
I
I*
h
t
f
^
I
I*
I
ItV
li
il'e
i^
iH
Planer Head Bolts and Nuts
C
D rT^~T1
Diameter of Bolt
No. of Threads per Inch
Short Diameter of Head
Length of Head
Short Diameter of Nuts
Thickness of Nuts
Washers for Planer Head Bolts,
Diameter of Washers
Thickness of Washers
h
t\
1
H
12
12
12
12
I
I
ij
li
t\
fV
1
f
I*
li
li
li
1
i
■i
'i
h
1^6
i
H
I^
It'.
A
ii^
T^^
tV
t'-z
rV
III
3\
3o8 BOLTS, NUTS AND SCREWS
Depths to Drill and Tap for Studs
Dia. of Stud
Dia. of Drill C. I.
Depth of Thread.
Depth to Drill
A
}
^
1
t\
^
1%
f
1
^
B
H
H
5
i
u
6 4
-f
fi
f
C
*
r?,
1^
H
i
H
-t
li
IT^W
D
r'l
7
'3"2
1
IS
H
it
l3^2
li
1X^6
I
5 5
If
Bolt Heads for Standard T-Slots
I ■
B
Dia.
Width
Thickness
Width
Width
Depth
Maximum
of
of
of
of
of
of
Depth with
Bolt
Head
Head
Slot
Slot
Slot
St'd Cutter
A
B
C
D
E
F
G
1
4
T6
i
f\
f
^2
f
5
T6
^
1%
f
H
3\
i\
f
1^
T6
H
j'j.
T6
t\
It
_9_
T%
i
li
1
1
ItV
-1
f
f
li
^
f
^rs
-1
I
1-
'tV
t
7
8
I f
-i
1X^6
i
lit
f
I
I 1
it
ixV
EYE BOLTS AND COTTER PINS
309
Eye Bolts
A
B
C
D
E
F
G
f
2
1
7
A
1
T%
h
2*
I
i
h
f
2i
li
li-
A
1
^
2I
lT6
t\
ii
■t%
1
2i
iH
lt
i
1
1
2f
li
re
i
4
l|
2|
2 J
l|
if
3
2 1
^
li
i
if
3l
2i
ij
T%
lA
I
I^
3i
2f
2
f
ItV
if
3l
3
2i
ii
I f
li
if
3i
3i
2-;:
f
i^
li
l|
3f
3h
25
if
If
lA
2
3f
3f
2i
1
If
If
Spring Cotters
No. of Wire Gage
it0 2
12
it0 2
II
Jt0 2i
i£.
jij
ii
7
f t0 3
6
Dia. Inches
1^3
No. of Wire Gage
5
I to 3
4
I to 4
I
2 to 6
f
3 to 6
Regular Lengths vary by J inch up to 4 inches and by i inch from 4 to 6 inches.
Lengths are measured under the eye.
3IO
BOLTS, NUTS AND SCREWS
Round ai-jd Square Washers
U. S. Standard Washers
Size of
Bolt
Size of
Hole
Outside
Diam-
eter
A
i
A
i
A
3
4
A
1
i
f
tV
I
tV
i
li
h
A
If
T%
f
li
f
H
If
f
it
2
1
if
2i
ItV
2i
I|
li
2f
li
If
3
If
li
3i
li
If
3i
If
If
3f
If
i|
4
l|
2
4i
2
2i
4i
2i
2f
4l
2^
2f
5
Thickness
Wire Gage
No.
l8 (A)
i6 (tV)
i6 (A)
14 (e\)
14 (/t)
12 (^,)
12 (j\)
io(i)
io(i )
9 (/o)
9(^)
9 (3\)
9 (A)
8 (iD
sai)
8(H)
8(ii)
8 (ii)
8(H)
6(A)
5(3^)
Narrow Gage Washers
Size of
Bolt
Size of
Hole
Outside
Diam-
eter
i
A
5
8
A
f
f
§
A
7
A
^
I*
i
A
li
^
if
f
-|
li
1
T6
If
^
-l
2
lA
2i
li
li
2-^
if
2f
if
li
3
li
if
3i
Thickness
Wire Gage
No.
l6 (A)
l6 (A)
l6 (A)
14 (6\)
12 (A)
12 (A)
loa )
loa)
9 (A)
9 (A)
8(H)
8(H)
Square Washers
standard sizes
Size of
Bolt
Size of
Hole
Width
f
A
li
A
^
If
1
A
2
f
11
2i
f
|4
2*
1
H
3
I
lA
3+
li
4
li
ig
4i
If
I*
5
i^
6
if
i|
6
2
2?
6
Thickness
1
WASHERS AND SCREW GAGE
311
Cast-Iron Washers
Size of
Bolt
Outside
Diameter
Thickness
Size of
Bolt
Outside
Diameter
Thickness
t
li
■h
li
4i
h
2
i
5
ij
i
2i
I
Sh
I
3
1
l|
6
If
1
3i
f
I4
7
li
I
'
i
2
7i
If
Riveting Washers
Size
of
Rivet
Size
of
Hole
Outside
Diam-
eter
Thick-
ness
Size
of
Rivet
Size of
Outside
Thickness
Wire
Gage
Hole
Diameter
Wire Gag
7 (.180)
fV
*
18
1
M
li
12
6 (.203)
i2
tHt
18
T^^
M
I
14
5 (-220)
n
^
18
t'«
M
I4
12
i
1
16
*
ii
Is
12
i
7
16
*
il
li
12
A
-^
1
14
1
}l
l|
II
T%
1
14
f
II
l§
JI
^|-
1
14
^
fi
If
10
f
-0 2^
I
14
Machine and Wood Screw Gage
No. of
Size of
No. of
Size of
No. of
Size of
No. of
Size of
Screw
Number in.
Screw
Number in
Screw
Number in
Screw
Number in
Gage
Decimals
Gage
Decimals
Gage
Decimals
Gage
Decimals
000
.03152
12
.21576
25
.38684
38
•55792
00
.04468
13
.22892
26
.40000
39
•57108
0
.05784
14
.24208
27
.41316
40
.58424
I
.07100
15
25524
28
.42632
41
•59740
2
.08416
16
.26840
29
.43948
42
.61056
3
■OQ732
17
.28156
30
•45264
43
.62372
4
.11048
18
.29472
31
.46580
44
.63688
5
.12364
19
.30788
32
.47896
45
.65004
6
.13680
20
.32104
33
.49212
46
.66320
7
.14996
21
•33420
34
.50528
47
.67636
8
.16312
22
•34736
35
.51844
48
.68952
9
.17628
23
.36052
36
.53160
49
.70268
10
.18944
24
.37368
37
.54476
5°
•71584
II
.20260
The difference
between co
nsecutive si
zes IS .01
J16"
312
BOLTS, NUTS AND SCREWS
Gimlet Point
Coach and Lag Screws
Diameter Screw
No. of Threads per Inch . . .
Across Flats Hex. and
Square Heads
Thickness Hex. and Square
Heads
lO
9i
1
7
7
6
5
1
5
f
4i
Ah
1
M
A
fi
1
II
^1
i|
lA
t\
\
tV
f
tV
i
H
1
f
li
Lengths of Threads on Coach and Lag Screws
or all diameters
Length of Screw
Length of Thread
Length of Screw
Length of Thread
ir
To Head
5 "
A" '
?"
ir
Sh"
A"
2Y
2 "
6 ''
a¥
• 3"
^Y
7 "
s"
3¥
2^'
8 ''
6 "
A"
Z"
9 ''
6 "
a¥
2>¥
lO to 12''
1"
Lag-Screw Test
(screws drawn out of yellow pine)
Test by Hoopes and Townsend
Diameter Screw.
Depth in Wood
Force in Pounds
\m.
tin.
fin.
iin.
3iin-
4 in.
4 in.
5 in.
4,960
6,000
7,685
11,500
I m.
6 in.
12,620
WOOD SCREWS
3^3
WOOD SCREWS
Wood screws range in size from No. o to No. 30, by the American
Screw Company's gage and in lengths from \ inch to 6 inches. The
increase in length is by eights of an inch up to i inch, then by quar-
ters of an inch up to 3 inches and by half inches up to 5 inches. As
a rule the threaded portion is about seven tenths of the total length.
The included angle of the flat head is 82 degrees. The table below
gives the body and head diameters, and the threads per inch as gen-
erally cut, although there is no fixed standard as to number of threads
which is universally adhered to by all wood-screw manufacturers.
Flat headed wood-screws include the head in the length given.
With round headed screws, one half the head is generally included
in the length although the practice is not uniform.
r^
t
Wood-Screw Dimensions
(angle of flat head = 82 degrees)
^
^
t
fc
g
a
a
^ (U
Diameter of
Diameter of
tn
'^ a;
Diameter of
Diameter of
-§
•si
Screw
Head
l-s
^^
Screw
Head
s-s
60
2: c5
dO
M>^
Z
H
2i
H
0
.05784
tV-
.110
^4 +
32
16
.26840
H +
.526
u-
9
I
.07100
5
64
.136
e\-
28
17
.28156
^%
•552
ff +
9
2
.08416
6^ +
.162
^2 +
26
18
.29472
il-
.578
3-1
8
3
.09732
A +
.188
A
24
19
.30788
A-
.604
If "~
8
4
.11048
/? +
.214
A-
22
20
.32104
ti-
•630
f +
8
5
.12364
i -
.240
H +
20
21
.33420
li +
.656
fl
8
6
.13680
j\-
.266
k +
18
22
.34736
M +
.682
H-
7
7
.14996
A-
.292
if-
16
23
.36052
If
.708
lf +
7
8
.16312
A +
.318
A +
15
24
.37368
1 -
•734
11
7
9
.17628
H +
•344
M +
14
25
.386S4
If —
.760
n-
7
10
.18944
A +
•370
1 -
13
26
.40000
|v —
.786
ff +
6
II
.20260
M-
.396
If +
12
27
.41316
M +
.812
i-i
6
12
.21576
S-
.422
U
II
28
.42632
11 +
.838
11-
6
13
.22892
if-
.448
11-
II
29
.43948
tV +
.864
M +
6
14
.24208
i-
.474
M +
10
30
.45264
■> q
n
.890
U
6
IS
.25524
i +
.500
i
10
314
BOLTS, NUTS AND SCREWS
U. S. Navy Boiler Rivets
U-
<--A ■■>
A
B
c
D
Weight of
10 heads
Weight per
inch of
shank L
\
H
1^
§
• 531
■ 0556
■h
I
h
A
.713
.0704
f
li
A
f
1.007
.0869
H
li
f ■
H
1-372
.1052
f
lA
1
f
1. 551
.1251
H
ii^
H
H
2.033
.1470
1
i^
H
i
. 2.258
.1703
H
if
3
H
2.871
.1956
I
If
H
I
3.5B4
.2225
1^
iH
if
lA
3.910
.2512
If
iM
1
li
4.761
.2816
ii^
2
i
lA
5.170
.3137
li
2|
H
If
6.215
.3477
lA
2f
I
lA
7.391
.3833
If
2|
lA
If
8.490
.4207
Irs
2|
li
lA
9.941
.4599
ij
2|
lA
li
11.507
.5006
lA
2f
Is
lA
13.242
.5433
If
2|
lA
If
15.146
.5876
iH
3
If
iH
17.300
.6336
If
3i
11%
If
19.485
.6815
U. S. Navy Hull and Tank Rr^t Heads
I<-D-H
PAN-HEAD
< A >
BUTTON
Pan-head
Button
Countersunk
A
B
c
D
A
B
C
A
B
c
D
A
A
\
i
A
A
\
I
A
60
f
A
\
i
f
A
\
f
A
60
H
f
\
\
if
f
\
if
\
60
I
A
f
\
I
A
1
lA
\
60
lA
\
f
f
lA
\
f
lA
\
45
lA
A
8
\
lA
A
1
lA
ii
45
I
li
f
I
I
li
f
I
If
if
37
li
If
H
I|
li
If
H
i|
If
if
37
ij
iH'
f
li
x\
lit
\
If
Iff
I
37
ROUND HEAD RIVETS
315
LENGTH OF ROUND HEAD RIVETS FOR DIFFERENT
THICKNESSES OF METAL
To find the required length of a rivet when tliickness of metal
between rivet heads is given, assuming the rivet hole to be yV i^ich
larger than the rivet before it is heated, refer to the table below.
Grip in inches means thickness of metal between rivet heads.
Diameter in Inches
Grip
in
i
f
1
1
I
Inches.
Length in Inches.
f
i^
If
i|
2
2i
if
i|
2
2|
2i
3
4
if
2
2|
2j
2f
1
l|
2|
2i
2f
2
2
2i
2!
22^
2;
u
2|
2f
2t
2f
2v
li
2;:
2|
2f
2f
2|
If
2f
2f
2|
3
2 •
2|
3
3i
31
if
2i-
3
3i
3i
si
ll
2|
3l
3i
3l
S2
ll
3
si
3l
3l
si
2
- 3l
si
3§
3l
si
2|
3i
3I
3f
3f
sl
2j
3f
3f
3f
sl
4
2I
3I
3f
3I
4
4i
2I
4
Si
4
4i
4i
2|
3f
4
4i
4i
4f
2f
3l
4i
41
4f
4I
2|
4
4i
4-
4I
4f
3,
4i
4|
4f
4f
4l
3I
4t
4-1
4f
4l
5
3l
4l
4f
4l
5
5i
3f
4f
4l
5
5i
5i
3l
< 3
5
5i
5i
5f
4
4I
5i
4
5f
5I
si
5
Si
5f
5^
5f
si
58
5f
4
5f
4
4
54
5I
5f
5f
5l
41
52
5f
5I
6
61:
4i
54
6
6i
6f
6|
4f
6-
61
6i
6f
6f
5
6-
61
6f
61
7
CALIPERING AND FITTING
THE VERNIER AND HOW TO READ IT
This method of measuring or of dividing known distances into
very small parts is credited to the invention of Pierre Vernier in 163 1.
The principle is shown in Figs, i to 3 and its application in Figs. 4
and 5. In Figs, i and 2 both distances o-i are the same but they
are divided into different divisions. Calling 0—1 = 1 inch then in
Fig. I it is clear that moving the lower seal one division will divide
0 J^ 1
FIG. I
0 ^ ^ 1
FIG. 2
ll
1 I 3
0 2
FIG. 3
I I I I
i 1 I ^ 4 =
FIG. 4
4 6
FIG. 5
Vernier Reading
the upper one in half. In Fig. 2 the upper scale is divided in half
and the lower one in thirds. If the lower scale is moved either way
until i or f comes under the end line, it has moved ^ of an inch
but if either of these are moved to the center line then it is only
moved ^ of this amount or ^
Figure 3 shows the usual application of the principle except that it
is divided in four parts instead of ten. Here both the scales have
four parts but on the lower scale the four parts just equal three parts
of the upper scale. It is evident that if we move the lower scale so
that o goes to i and 4 goes to 4 that it will be moved J the length
of the distance o — 4 on the upper scale. If this distance was i inch,
each division on the upper scale equals J inch and moving the lower
scale so that the line i just matches the line next to o on the upper
scale gives J of one of these divisions or -^ of an inch.
316
MEASURING THREE-FLUTED TOOLS
317
Figures 4 and 5 show the usual appHcation in which the lower or
vernier scale is divided into 10 parts which equals 9 parts of the
upper scale. The same division holds good, however, and when
the lower scale is moved so that the first division of the vernier just
matches the first line of the scale, it has been moved just one
tenth of a division. In Fig. 4 the third lines match so that it has
moved j^ and in Fig. 5, j"^ of a division. So if A B is one inch then
each division is jq" of ^^ i^ch and each line of the vernier is yo of
that or Y^o of an inch.
To find the reading of any vernier, divide one division of the upper
or large scale by the number of divisions in the small scale. So if
we had a vernier with 16 divisions in each, the large scale being
I inch long, then the movement of one division is j^ of jg or aie of
an inch.
READING THE MICROMETER
The commercial micrometer consists of a frame, the anvil or fixed
measuring point, the spindle which has a thread cut 40 to the inch
on the portion inside the sleeve or barrel and the thimble which
goes outside the sleeve and turns the spindle. One turn of the
A — Frame
B - Anvil ^
C - Spindle or Screw
D - Sleeve or Barrel
E- Thimble
Fig. 6. — Micrometer
screw moves the spindle 4V or .025 of an inch and the marks on the
sleeve show the number of turns the screw is moved. Every fourth
graduation is marked i, 2, 3, etc., representing tenths of an inch or
as each mark is .025 the first four means .025 X 4 = -loo, the third
means .025 X 4 X 3 = .300.
The thimble has a beveled edge divided into 25 parts and num-
bered o, 5, 10, 15, 20 and to o again. Each of these mean ^^5 of a
turn or 2V of 4V = toVcT of an inch. To read, multiply the marks
on the barrel by 25 and add the graduations on the edge of the
thimble. In the cut there are 7 marks on the sleeve and 3 on the
thimble so we say 7 X 25 = 175, plus 3 = 178 or .178.
In shop practice it is common to read them without any multiply-
ing by using mental addition. , Beginning at the largest number
3i8
CALIPERING AND FITTING
shown on the sleeve and calling it hundreds and add 25 for each
mark, we say in the case show 100 and 25, 50, 75 and then add the
numbers shown on the thimble 3, making .178 in all. If it showed
4 and one mark, with the thimble showing 8 marks, the reading
would be 400 + 25 + 8 = 433 thousandths or .433.
THE TEN-THOUSANDTH MICROMETER
This adds a vernier to the micrometer sleeve or barrel as shown
in Fig. 7, which is read the same as any vernier as has been ex-
plained. First note the thousandths as in the ordinary micrometer
and then look at the line on the sleeve which just matches a line on
Thimble
II II
Inn II J
43210
Sleeve
Thimble
M I III I Mil
098'654 32:
Sleeve
B
Fig. 7. — Micrometer Graduations
the thimble. If the two zero lines match two lines on the thimble,
the measurement is in even thousandths as at B which reads .250.
At C the seventh line matches a line on the thimble so the reading
is .2507 inch.
MEASURING THREE-FLUTED TOOLS WITH
THE MICROMETER
The sketch, Fig. 8 on page 319, shows a V-block or gage for
measuring three-fluted drills, counterbores, etc.
The angle being 60 degrees, the distances A, B, and C are equal.
Consequently to determine the correct diameter of the piece to be
measured, apply the gage as indicated in the sketch and deduct
one third of the total measurement.
The use of this gage has a decided advantage over the old way
of soldering on a piece of metal opposite a tooth or boring out a ring
to fit to.
Using a standard 60-degree triangle for setting and a few different
sizes of standard cylindrical plug gages for testing, the V-block
may be easily and very accurately made.
LIMITS FOR FITS
319
TJ
I'lli!
Fig. 8. — Measuring Three-Fluted Tools
PRESS AND RUNNING FITS
Parallel Press, Drive and Close Fits
Table i, page 320, gives the practice of the C. W. Hunt Company,
New York, for press, drive and close or hand J&ts for parallel shafts
ranging between one and ten inches in diameter. In accordance with
general practice, the holes for all parallel fits are made standard, except
for unavoidable variation due to the wear of the reamer, the variation
from standard diameter for the various kinds of fits being made in
the shaft. This variation is, however, not positive, but is made
between limits of accuracy or tolerance. Taking the case of a press
fit on a two-inch shaft, for example, it will be seen that the hole — •
that is, the reamer — is kept between the correct size and 0.002 inch
below size, while the shaft must be between 0.002 and 0.003 i^ich
over size. For a drive or hand fit the limits for the hole are the
same as for a press fit, while the shaft in the former case must be
between o.ooi and 0.002 large and in the latter between o.ooi and
0.002 small.
Parallel Running Fits
Table 2, page 321, gives in the same way the allowances made by
the same concern for parallel running fits of three grades of close-
ness. The variations allowed in the holes are not materially dif-
ferent from those of the preceding table, but the shafts are, of
course, below instead of above the nominal size.
In all cases the tables apply to steel shafts and cast-iron wheels or
other members. In the right-hand columns of the tables the for-
mulas from which the allowances are calculated are given, and from
which the range of tables may be extended.
320
CALIPERING AND FITTING
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LIMITS FOR GAGES
321
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322
CALIPERING AND FITTING
Shrink Fits
Table 3 gives the practice of the General Electric Company,
Schenectady, New York, in regard to shrink fits, the same allowances
also being made for press fits on heavy work such as couplings, etc.
Table ■z. Allowances for Shrink Fits
Dia. In.
Allowance
Dia. In.
Allowance
Dia. In.
Allowance
I
.001
20
.008
42
.0143
2
.0015
22
.0088
44
.015
3
.0020
24
.0093
46
•0155
4
.0028
26
.0098
48
.016
6
•0035
28
.0105
60
.020
8
.0045
30
.oil
72
.024
10
.0053
32
.0115
84
.027
12
.0058
34
.012
96
.030 .
14
.0065
36
.0128
108
•033
16
.007
38
•0133
120
•0355
18
.0075
40
.0138
132
144
.038
.040
LIMITS FOR GAGES
The Newall Engineering Company, when developing their system
of limit gages, investigated the practice of the leading English,
Continental and American engineering concerns relative to allowances
for different kinds of fits and prepared a table which is the average
of all the data received, every point included being covered by the
practice of some prominent establishment. The limits and allow-
ances thus arrived at for shop gages are given in Table 4, which is
self-explanatory.
Table
Limits and Allowances in Shop Gages for
Different Kinds of Fits
Nominal Diameters
Over size .
Under size
Margin . . .
,00025
,00025
000 !;o
00050
00025
00075
,00075
,00025
,00100
001 00
00050
00150
,00100
,00050
,00150
OOIOO
00050
.00150
,00050
,00200
Limits in Plug Gages for Standard Holes
(Table Continued an Page 323)
ALLOWANCES FOR FITS
323
Table 4 Continued. — Limits in Shop Gages
Allowances — over Standard — for Force Fits
Nominal Diameters
Mean . .
High . .
Low. . .
Margin
00075 -ooiys
ooioo .00200
00050 .00150
00050 .00050
.00350
.00400
.00300
.00100
00525
00600
00450
.00700
.00800
.00600
001501.00200
,00900
,01000
,00800
,00200
6"
OIIOO
,01200
,01000
,00200
Allowances — over Standard — for Driving Fits
Nominal Diameters §"
Mean . .
High . .
Low . .
Margin
000375
00050
00025
00025
,000875
OOIOO
00075
,00025
.00125
.00150
.00100
.00050
00200
00250
00150
OOIOO
,00250
.00300
.00200
.00100
.00300
.00350
.00250
.00100
.00350
.00400
.00300
.00100
Allowances — Below'Standard — for Push or Keying Fits
Nominal Diameters
High . .
Low . . .
Margin
,00025
,00075
,00050
,00050
,00100
,00050
OOIOO .00150 .00200
,00150 .00200 .00250
,00050 .00050 .00050
,00200
,00250
,000501.00050
Clearances for Running Fits
Class of
Gage
Diameters
r
'
2"
3"
4"
5"
6"
Mean
.00150
.00200
.00260
.00320
.00380
.00440
.00500
X.
1 High
.00100
.00125
.00175
.00200
.00250
.00300
.00350
Low
.00200
.00275
.00350
.00425
.00500
•00575
.00650
I Margin
.00100
.00150
.00175
.00225
.00250
.00275
.00300
Mean
.00100
.00150
.00190
.00230
.00270
.00310
.00350
Y.
High
.00075
.00100
.00125
.00150
.00200
.00225
.00250
Low
.00125
.00200
.00250
.00300
.00350
.00400
.00450
I Margin
.00050
.00100
.00125
.00150
.00150
.00175 -00200
("Mean
.000625
.00100
.00120
.00140
.00160
.00180
.00200
Z.
High
.00050
.00075
.00075
.00100
.00100
.00125
.00125
Low
.00075
.00125
.00150
.00200
.00225
.00250
.00275
I Margin
.00025
.00050
.00075
.00100
.00125
.00125
.00150
Class X is suitable for engine and other work requiring easy fits.
Class Y is suitable for high speeds and good average machine work.
Class Z is suitable for fine tool work.
324 CALIPERING AND FITTING
Limits For Work Ground to Various Classes of Fits
Table 5 gives the limits used by the Brown and Sharpe Manu-
facturing Company in grinding work to various classes of fits required
in machine manufacture.
Table 5 — Grinding Limits for Cylindrical Pieces
As Adopted by Brown and Sharpe Mfg. Co.
RtTNNING FITS — ORDINARY SPEED
To |-inch diameter, inc 0.00025 to 0.00075 Small
To i-inch diameter, inc 0.00075 to 0.0015 Small
To 2-inch diameter, inc 0.0015 to 0.0025 Small
To 3|-inch diameter, inc 0.0025 to 0.0035 Small
To 6-inch diameter, inc 0.0035 to 0.005 Small
RUNNING FITS — HIGH SPEED, HEAVY PRESSURE AND ROCKER SHAFTS
To ^-inch diameter, inc 0.0005 to o.ooi Small
To i-inch diameter, inc o.ooi to 0.002 Small
To 2-inch diameter, inc 0.002 to 0.003 Small
To 3 ^-inch diameter, inc 0.003 to 0.0045 Small
To 6-inch diameter, inc 0.0045 to 0.0065 Small
SLIDING FITS
To ^-inch diameter, inc 0.00025 to 0.0005 Small
To I-inch diameter, inc 0.0005 to o.ooi Small
To 2-inch diameter, inc o.ooi to 0.002 Small
To 3^-inch diameter, inc 0.002 to 0.0035 Small
To 6-inch diameter, inc 0.003 to 0.005 Small
STANDARD FITS
To ^-inch diameter, inc Standard to 0.00025 Small
To I-inch diameter, inc Standard to 0.0005 Small
To 2-inch diameter, inc Standard to o.ooi Small
To 3|-inch diameter, inc Standard to 0.0015 Small
To 6-inch diameter, inc Standard to 0.002 Small
DRIVING FITS — FOR SUCH PIECES AS ARE REQUIRED TO BE READILY
TAKEN APART
To ^-inch diameter, inc Standard to 0.00025 Large
To I-inch diameter, inc 0.00025 to 0.0005 Large
To 2-inch diameter, inc 0.0005 to 0.00075 Large
To 3^-inch diameter, inc 0.00075 to o.ooi Large
To 6-inch diameter, inc o.ooi to 0.0015 Large
DRIVING FITS
To ^-inch diameter, inc 0.0005 to o.ooi Large
To I-inch diameter, inc o.ooi to 0.002 Large
To 2-inch diameter, inc 0.002 to 0.003 Large
To 35-inch diameter, inc 0.003 to 0.004 Large
To 6-inch diameter, inc 0.004 to 0.005 Large
METRIC ALLOWANCES FOR FITS 325
Table 5 Continued
FORCING FITS
To ^-inch diameter, inc 0.00075 to 0.0015 Large
To i-inch diameter, inc 0.0015 to 0.0025 Large
To 2-inch diameter, inc 0.0025 to 0.004 Large
To 3|-inch diameter, inc 0.004 to 0.006 Large
To 6-inch diameter, inc 0.006 to 0.009 Large
SHRINKING FITS — FOR PIECES TO TAKE HARDENED SHELLS f INCH
THICK AND LESS
To |-inch diameter, inc 0.00025 to 0.0005 Large
To i-inch diameter, inc 0.0005 to o.ooi Large
To 2-inch diameter, inc o.ooi to 0.0015 Large
To 3^-inch diameter, inc 0.0015 to 0.002 Large
To 6-inch diameter, inc 0.002 to 0.003 Large
SHRINKING FITS — FOR PIECES TO TAKE SHELLS, ETC., HAVING A
THICKNESS OF MORE THAN f INCH
To |-inch diameter, inc 0.0005 to o.ooi Large
To I-inch diameter, inc o.ooi to 0.0025 Large
To 2-inch diameter, inc. 0.0025 to 0.0035 Large
To 3|-inch diameter, inc 0.0035 to 0.005 Large
To 6-inch diameter, inc 0.005 to 0.007' Large
GRINDING LIMITS FOR HOLES
To ^-inch diameter, inc Standard to 0.0005 Large
To I-inch diameter, inc Standard to 0.00075 Large
To 2-inch diameter, inc Standard to o.ooi Large
To 3|-inch diameter, inc Standard to 0.0015 Large
To 6-inch diameter, inc Standard to 0.002 Large
To 12-inch diameter, inc Standard to 0.0025 Large
Metric Allowances For Fits of All Classes
Table 6 covers allowances worked out by the Newall Engineering
Company for use in connection with metric measurements; the
allowances being given in decimals of a millimeter.
The Newall system is based on a hole "basis," which means that
all holes are produced as near the standard size as commercially
possible and the allowances are made in the shaft or other fitting.
The first part of the table shows the tolerances allowable in a standard
hole for two grades of work which are designated by classes A and B.
The remainder of the table covers fits of various classes.
326
CALIPERING AND FITTING
Table 6 — The Newall Standard
Tables of Allowances for Various Classes of Fits in Millimeters
Tolerances in Standard Holes for Two Grades of Work
Nominal Dia.
Up to 15 1 16-25
26-50
51-75
76-100
IOI-I25
126-150
High limit
Low limit
Tolerance
+ 0.007
— 0.007
0.014
+ 0.013
— 0.007
0.020
+ 0.019
— 0.007
0.026
+ 0.026
- 0.013
0.039
+ 0.026
— 0.013
0.039
+ 0.026
— 0.013
0.039
+ 0.039
— 0.013
0.052
High limit
Low limit
Tolerance
+ 0.013
— 0.013
0.026
+ 0.019
- 0.013
0.032
+ 0.026
— 0.013
0.039
+ 0.032
— 0.019
0.052
+ 0.039
— O.OIQ
0.058
+ 0.045
— 0.019
0.064
+0.051
— 0.026
0.077
Force and Shrink Fits
-
Nominal Dia.
Up to 15
16-25 1 26-50
51-75
76-100
101-125
126-150
High limit
Low limit
Tolerance .....
+ 0.026
+ 0.013
0.013
+ 0.051 1 + 0.102
+ 0.038 + 0.077
0.013' 0.025
+ 0.153
+ 0.115
0.038
+ 0.204
+ 0.152
0.052
+ 0.255
+ 0.203
0.052
+ 0.306
+ 0.254
0.052
Driving
Fits
Nominal Dia.
Up to 15
16-25
26-50
51-75
76-100
101-125
126-150
High limit
Low limit
Tolerance
+ 0.013
+ 0.007
0.006
+ 0.026
+ 0.019
0.007
+ 0.039
+ 0.026
0.013
+ 0.064
+ 0.039
0.025
+ 0.077
+ 0.051
0.026
+ 0.089
+ 0.063
0.02C
+ 0.102
+ 0.076
0.026
Push Fits
— Go in Easy but wiU not Turn
Nominal Dia.
Up to 15
16-25
— 0.006
— 0.019
0.013
26-50
51-75
76-100
101-125
126-150
High limit
Low limit
Tolerance
— 0.006
— 0.019
0.013
— 0.006
— 0.019
0.013
— 0.012
— 0.026
0.014
— 0.012
— 0.026
0.014
— 0.012
— 0.026
0.014
— 0.012
— 0.026
0.014
Running Fits for Engine and Similar Work
Nominal Dia.
Up to 15
16-25
26-50 SI-7S
76-100
101-125
126-150
High limit ....
Low limit
Tolerance
- 0.025
- 0.051
0.026
— 0.032
— 0.070
0.038
— 0.045 — 0.051
— 0.090 — 0.108
0.045 0.057
— 0.063
— 0.127
0.064
— 0.076
- 0.146
0.070
- 0.089
- 0.16s
* 0.076
Running Fits for Good Average Machine Work
Nominal Dia.
Up to .15 16-25 ■ 26-50
51-75
76-100
101-125
126-150
High Umit ....
Low limit
Tolerance
1
— 0.019 —0.0251 —0.032
— 0.032' —0.051 —0.064
0.013 1 o.o26| 0.032
— 0.038
— 0.076
0.038
— 0.051
- 0.089
0.038
- 0.057
— O.IOI
0.044
- 0.063
— 0.II4
0.051
Running Fits for Fine Tool Work
Nominal Dia.
Up to 15
16-25
26-50
51-75
76-100
101-125
126-150
High limit ....
Low Mmit
Tolerance
— 0.012
— 0.019
0.007
— 0.019
— 0.032
0.013
— 0.019
- 0.039
0.020
— 0.025
— 0.051
0.026
— 0.025
- 0.057
0.032
- 0.032
— 0.064
0.032
- 0.032
— 0.070
0.038
RUNNING FITS FOR POWER MACHINERY 327
Press Fits For Wheel Hubs
The practice of the Boston Elevated Railroad is to allow 8 tons
per inch of diameter. An excess of 2 tons total pressure is allowed
for cast iron, while the minimum pressure may be from 8 to 13 tons
belov/ the normal according to diameter, as shown by the following
table. These are for cast iron hubs \^ith the cone 5 inches in diam-
eter — 7I inches long. For cast steel or wrought iron 20 per cent
greater pressure is allowed.
Diameter of
Fit
Minimum
Pressure
Maximum
Pressure
Variation
AUowed
in Tons
2itO 2if
12
22
3, to 3t\
16
26
3lto 3-f
4 to 4tV
4^ to 4]|
20
24
28
30
34
38
10
5 to 5tV
5ito sH
31
35
42
46
II
6 to 61V
6ito 6i|
38
42
50
54
12
7 to 7tV
7lto 7it
45
49
58
62
13
8 to 81^
8^0 8i|
52
56
66
70
14
9 to 9 A
9^ to gfl
10 to lOxV
59
63
67
74
78
82
15
RUNNING FITS FOR POWER TRANSMISSION
MACHINERY
The Dodge Manufacturing Company has different standards
for different classes of work for running fits. Their ordinary bear-
ings vary from g^j inch for i inch to a little over -jV for 6 inches.
Their clutch sleeves, which are babbitted, run very much closer,
varying from 0.008 to about 0.0015 inch. Loose pulleys are some-
times made as close as 0.003 inch on the smaller sizes. The com-
pany has found that a good standard on loose pulleys is about gV
on a 2^ inch hole and varying proportionately for diameters above
and below that. This is very much freer than most people
recommend, but it has been found that in the general trade there
is more difficulty in having a little too tight a fit than there is in
having the fit a little too loose.
328
CALIPERING AND FITTING
MAKING ALLOWANCES WITH THE CALIPERS FOR
RUNNING, SHRINK, AND PRESS FITS
One of the familiar devices of the machinist consists in giving
the inside calipers a certain amount of side play, when it is desir-
able to obtain a measure minutely less than the full diameter of the
hole, as in making a loose or running fit, or a sliding fit as of a
plunger in a cylinder. Thus in Fig, g, A is the diameter of the bore, B
the caliper setting and C the side play permitted the caliper in the hole.
In the table below is given a list of the reduced dimensions for
different amounts of side play of the calipers in a 12-inch hole.
From this, the dimensions may be obtained for holes of other diam-
eters by division. Where in the table the side play is 2 inches, if
we divide the items by 4 we have the side play and the reduced
dimension for a 3-inch hole, or 0.5 inch and 2.9894 inches respectively.
Fig. 9. — Side Play of the Calipers
Table of Reduced Diameters Indicated by Inside Calipers
FOR Different Amounts of Side Play in a i 2-inch Hole
Side play
0.1 11.9999
0.2 II. 9991
0.4 11.9983
0.6 11.9962
0.8 11.9933
i.o 11.9895
1.2 11.9849
1.4 11-9795
1.6 11.9730
1.8 11.9660
2.0 11-9579
2.2 .11.9490
2.4 II-939I
2.5 11.9339
3.0 r r • • • 11-904'^
CALIPER SIDE PLAY
329
Axial Inclination of the Calipers in Measuring for Shrink or
Press Fits
In the case worked out on page 328, it was desired to produce a hole
slightly larger than the piece to go into it, or a piece slightly smaller
than the hole. In operations where a hole is wanted somewhat smaller
than the piece to be shrunk or pressed into ft, a similar plan of meas-
uring can be employed, and a table giving the tightness can be
computed. The sketch, Fig. 10, will serve to make the meaning clear.
The distance A is the diameter of a hole and line a is the length of
a gage the exact size of the piece to be pressed or shrunk into the
hole. The distance b is the amount the gage lacks of assuming a
position square or at a right angle to the axis of the hole.
It is an easy matter to make a table as suggested. It is only
necessary to find the different lengths for the hypotenuse a for the
right-angle triangle of which A is the constant base and b the per-
pendicular, taking b at different lengths from | inch to 2 inches.
Assuming the diameter to be 12 inches, then the lengths indicated
for different inclinations in the direction of the axis will be as given
in the following table.
Fig. 10. — Inclination of the Calipers for Press Fits
Table for Axial Inclination of Calipers in Allowing for
Shrink or Force Fits in a i 2-inch Hole
Inclination of
calipers ^
i inch 12.00065
i inch 1 2.00260
f inch 12.00580
I inch 1 2.01040
t inch 12.01626
f inch 12.02340
I inch 12.03180
I inch 12.04159
ij inches 12.06490
I J inches 12.09338
if inches 12.12689
2 inches 12.16550
330 CALIPERING AND FITTING
Side Play of Calipers in Boring Holes Larger than a Piece
of Known Diameter
The following is an approximate rule for obtaining the variation
in the size of a hole corresponding to a given amount of side play
in the calipers. The rule has the merit of extreme simplicity and
can be applied equally well to all diameters except the very smallest.
In most cases the calculation is so simple that it can be done men-
tally without having recourse to pencil or paper.
The Calculation
Let A in Fig. 1 1 = side play of calipers or end measuring rod m
sixteenths of an inch.
B = dimensions to which calipers are set, or length of measuring
rod in inches.
C = difference between diameter of hole and length of B in
thousandths of an inch.
A^
Then C = —x, within a very small limit.
2/>
Fig. II. — Caliper Side Play
Example: A standard end measuring rod, 5^ inches long, has
I inch of side play in a hole. What is the size of the hole ? In this
case A = 6 and 5 = 5J. Apply the above formula:
C = = — = 3.27 thousandths of an inch, or 0.00327 inch.
II II
The diameter of the hole, therefore, is 5I + 0.00327 or 5.50327.
The method ^yill be found to be correct within a limit of about
0.0002 inch if the amount of side play is not more than one eighth
of the diameter of the hole for holes up to 6 inches diameter; within
0.0005 iJ^ch for holes from 6 inches up to 12 inches; and within o.ooi
for holes from 12 inches up to 24 inches.
DIMENSIONS OF KEYS AND KEY-SEATS 331
Allowing for Running and Driving Fits
This rule has been found to be useful for boring holes of large
diameters in which allowances have to be made for running or
driving fits, as only a single measuring rod for each nominal size is
required. The rods should be of standard length, or a known
amount less than standard, the allowances being obtained by varying
the amount of side play when boring. The rule is also capable of
determining limits, as the maximum and minimum amount of side
play allowable can be specified. The measuring rods should be
tapered at each end and the points slightly rounded. For accurate
work, the body of the rod should be encased in some non-conducting
material to nullify the effect of the heat of the hand.
In comparing this method with that described on page 330, it
should be remembered that the conditions are reversed — that is
to say, the first method is for setting calipers to a given dimension
smaller than a hole of known diameter, whereas the method now
described is for boring a hole a given amount larger than a gage of
known length.
In measuring the side play it is sufficient to take it to the nearest
sixteenth of an inch, and if anything like accuracy is required it
should be measured not guessed at.
DIMENSIONS OF KEYS AND KEY-SEATS
The following rules and table on page 332, as prepared by Baker
Bros., Toledo, Ohio, give dimension of keys and key-seats.
The width of the key should equal one fourth the diameter of the
shaft.
The thickness of the key should equal one sixth the diameter of
the shaft.
The depth in the hub for a straight key-seat should be one half
the thickness of the key.
The depth in the hub at the large end, for a taper key-seat, should
be three fifths the thickness of the key.
The taper for all key-seats should be -f-^ inch in i foot of length.
The depth to be cut in the hub for taper key-seats, at the large
end, is greater than those cut straight, for the reason that unless
this is done the depth in the hub at the small end will not be sufficient,
especially in long key-seats.
The depths of key-seats in the table are given in thousandths of
an inch and measured from the edge of the key-seat, and not from
the center. In this manner the exact depth of key-seat can be
measured at any time after it is cut.
For extra long key-seats the depth cut in the hub may be slightly
increased, but for the average work the table will be found correct.
2>Z2
CALIPERING AND FITTING
Dimensions of Keys and Key-Seats. (Baker Bros.)
Size of
Hole
Decimal
Preferred
Nearest
Preferred
Nearest
Depth to -n
be Cut in Ji
Hub for r
Straight *°'
Key
epth at
rge End
Equiv-
Width of
Size of
Thickness
Fractional
alent
Key-Seat
Cutter
of Key
Thickness
Taper
Key
I
I.
.25
i
.166
t\
.093
112
itV
1.062
.265
i
.177
♦
•093
112
li
1. 125
.281
i
.187
.093
112
lA
1. 187
.296
T^
.198
sV
.109
131
li
1.25
.312
^?
.208
J2
.109
131
H-"
1-312
.328
♦
.219
^2
.109
131
^%
1-375
•343
t
.229
i
.125
15
ii^
1-437
•359
1
•239
i
-125
15
^\
1-5
•375
1
•25
i
.125
15
lA
1.562
•39
f
.26
i
•125
15
if
1.625
.406
tV
.271
z%
.141
168
iH
1.687
.421
t\
.281
J%
.141
.168
if
1-75
•437
tV
.292
j\
.141
168
iH
1.812
-453
tV
.302
A
.141
168
il
1-875
.468
h
.312
-i
.171
206
lit
1-937
.484
h
•323
;f
.171
206
2
2.
•5
h
'333
.171
206
2tV
2.062
•515
i
.344
V-
.171
206
2i
2.125
•531
h
-354
i
.171
206
2A
2.187
•547
h
-364
^2
.171
206
2i
2.25
-563
h
-375
H
•171
206
2^
2.312
.578
h
-385
M
.171
206
2f
2.375
.593
f
•396
tV
.218
262
2tV
2.437
.609
.406
tV
.218
262
2^
2.5
-625
1
.416
tV
.218
262
2A
2.562
.641
1 .
•427
tV
.218
262
2f
2.625
.656
•I
•437
t\
.218
262
2H
2.687
.672
1
-448
t\
.218
262
2i
2-75
.687
1
-458
IV
.2l8
262
2H
2.812
•703
f
.469
tV
.218
262
2|
2.875
.719
f .
-479
i
•25
3
2H
2-937
•734
f
.49
h
•25
3
3
3-
•75
f
•5
h
•25
3
3i
3-125
.781
1
.521
h
•25
3
3A
3-187
-797
1
-531
h
•25
3
3i
3-25
.812
f
.542
h
•25
3
^\
3-375
-844
i
.562
1
•312
375
3tV
3-437
•859
1
-573
1
.312
375
3i
3-5
•875
7
8
•583
f
.312
375
3f,
3-625
.906
f
.604
1
•312
375
3H
3.687
.923
.614
.312
375
3f
3-75
.937
1
.625
f
•312
375
4.
3-875
.969
I
.646
li
-343
412
3il
3-937
.984
I
.656
li
-343
412
4
4.
I.
I
.666
IF
-343
412
STRAIGHT KEYS
333
DIMENSIONS OF STRAIGHT KEYS
Another system of keys used by a good many manufacturers is
given in the table following, the sizes of shafts ranging by sixteenths
from ■f'-Q inch to 4 inches and by eighths from 4 to 6 inches. The
keys are square until the i| inch shaft is reached, when the thickness
of the key becomes yV less than the width. With the 4^ size the
thickness of the key becomes | inch less than the width and this
difference is constant up to the 5J shaft when the width exceeds the
thickness by -^ inch, this difference in the two dimensions continu-
ing throughout the remainder of the table.
Dimensions of Straight Keys
>>
<M
•a
>.
t«
^
>.
^
>t
^
JS
t^
0
c3
^
0
t^
0
3
OJ
0
C/2
vi
C/3
«*-4
m
CO
«*H
^
w
<4-l
CO
"o
^
«*-!
0
al
tM
0
0
u
•3
•T3
ll
0
c5
rSi
■5
0
i
,5
Is-
.•2
ll
5
'^
H
,5
'^
H
Q
'^
H
Q
^
H
0
li
A
A
2^
i
tV
3f
1
11
tV
IT^
1^
A
2t^^
A
i
3il
f
-i
i
If
A
t\
2f
T%
J
3l
if
4
A
itV
^^
T%
2ii
A
i
3il
if
f
i
I^
A
t\
2|
¥
h
4
if
f
1%
3%
1%
lA
2H
i
4i
if
1
t
/.
j\
If
f
1
2|
t\
h
4i
i
i^
i
i
lii
1
f
2i|
1
A
4l
1
f
h
t
i
if
1
3
f
T%
4^
it
if
T%
i
i
lit
f
1
3t6
1
1%
4f
if
il
f
t\
T%
I5
T^e
1
3*
f
1%
4l
I
f
ii
j\
l\
lit
tV
■g
3tV
f
A
5
I
f
♦
t\
2
tV
3i
f
5i
itV
1
if
A
T^6
2tV
tV
1
3t\
ie
5i
ItV
7
8
1
T%
fV
2i
tV
f
31
16"
1
5i
ItV
7
8
H
2t\
i
1^
3tV
ii
1
si
li
T*
I
2i
h
1^
3i
i|
1
5f
li
-f
ixV
2tV
h.
A
3tf
H
5f
ll
H
li
2|
h
tV
3f
f
ii
5l
it\
I
it\
2tV
'
re
3H
^
ii
6
lA
I
SQUARE FEATHER KEYS AND STRAIGHT KEY SIZES
The tables on page 334 give the sizes of square feather keys and
regular straight keys in accordance with the practice of Jones &
Laughlin, Pittsburg, For taper keys, this concern and many others
use a |-inch per foot taper.
334 CALIPERING AND FITTING
Square Feather Key Sizes. (Jones & Laughlin)
Dia. of Shaft
Size of Key
Dia. of Shaft
Size of Key
I to l|
i X i
3T6 to 3I
ilx H
lA toil
AX A
3tV to 3f
1 X i
IjV to if
1 X f
3H to 3f
iix H
iji to i|
A X j\
3-1 to 4 J
I X I
I-f to 2j
i X ^
4t6 to 4|
itV X itV
23% to 2|
AX A
4t6 to 4f
ij Xii
2i^ to 2f
1 X f
4H to 5i
li X li
2H to 2|
iixH
5t6 to 5i
if X if
2lt to 3i
f X f
5ll to 6i
ih Xih
Straight Key Sizes.
(Jones & Laughlin)
Dia. of Shaft
Size of Key
Dia. of Shaft
Size of Key
I to li
i XA
3Ato3l
Hx il
iT^toif
A X 3V
3tV to 3f
i X if
itV to If
f X i
SH to 3l
iix t
iH to i|
A X j%
3Tt to 4i
I X H
lit to 2i
i XH
4A to 4f
lAx ii
2fV to 2|
AX t
4tV to 4l
li X f
2yV to 2f
f x^f
4H to 5i
li X tl
2H to 2|
11 X -f
5A to 5|
If X II
2if to 3i
1 X ^
5H to 6i
i| X I
The Earth Key
/ ,K
^
\
-w-
No. of Key
w
w
D
I
1
.132
tIs
2
A
.165
■ii
3
A
.199
*
4
1
.264
6\
5
A
.329
A
PRATT AND WHITNEY KEY SYSTEM
335
Keys made with
\ Bound Ends and
(
^ -m KejTfays Cut in
/. _y - Bpline MUler
_JIIIII'
:lii|i|-r. A ^ -) 1
f
-I^
3]^-?(^
The Length "L" may vary from the table given, but must at least
be equal to (2 X W). The maximum length of slot which can be
cut in the Sphne Milling machine in one cut; is (4" + W). Note
that the Width (W) is in all cases equal to the depth (D).
Pratt & Whitney Key System
Key
No.
L
w
H
D
No.
L
W
H
D
I
tV
A
tV
22
i
1
i
2
1
A
^^T
A
23
If
A
if
T^6
3
i
t\
i
F
f
T^6
1
4
A
6^1
A
24
1
1
i
5
1
i
j\
i
25
li
1^6
if
t\
6
/^
if
A
G
T%
f
7
i
T^.
i
51
1
4
f
1
4
8
i
/^
if
A
52
If
fV
if
t\
9
t\
/.
xV
S3
f
T^^
1
10
/2
if
A
26
t\ '
A
t\
II
1
A
¥2
t\
27
2
i
f
i
12
«
^.
fi
A
28
T^6
if
A
A
1
4
1
i
29
3
8
T^^
t
13
tV
3^2
A
54
i
f
1
14
I
aV
U
A
55
2i
1^
if
A
15
i
t
1
4
56
f
1^
B
A
if
A
57
tV
fi
A
16
¥
3\
A
58
A
if
t\
17
li
¥'2
2 1
64
A
59
ol
f
T^,I
f
18
i
3
8
i
60
22
iV
li
tV
C
t\
if
T^e
61
1
2
3
4
i
19
A
j\
T^,I
30
f
t\
1
20
s\
u
A
31
tV
¥
j^
21
li
1
4
1
I
32
3
i
1
D
A
if
A
33
A
fa
A
E
1
T%
f
34
f
il
f
336
CALIPERING AND FITTING
/
Shaft
Whitney Keys and Cutters. Nos. i to 26
(Woodrufif's Patent)
No. of
Key
and
Cutter
Dia. of
Cutter
Thick-
ness of
Key
and
Cutter
Length
Key
Key
Cut
Below
Cen-
ter
No. of
Key
and
Cutter
Dia.
of
Cut-
ter
Thick-
ness of
Key
and
Cutter
Length
Key
Key
Cut
Below
Cen-
ter
A
B
C
D
A
B
C
D
I
i
tV
1
^^
16
li
fV
li
/t
2
h
3\
i
17
li
^'^
li
«^T
3
h
i
i
"^4
18
li
1
4
li
6^?
4
^
j\
&
tV
c
i^
1^
i^
^
5
i
t
tV
19
li
fk
li
^4
6
f
i'2
*
tV
20
li
3V
li
6^T
7
f
i
1^«
21
li
i
li
K^T
8
1
^',
f
tV
D
li
A
li
<fV
9
-i
A
f
tV
E
li
i
li
If-T
10
'i
aV
i
tV
22
i^
i
it
3^*^
II
'i
t\
i
T^.
23
l|
T^.
It
^\
12
8
3%
^
1^6
F
l^
it
Ji
A
I
i
^
tV
24
li
1
i^
/?
13
I
^
I
25
l^
1^«
i^
^V
14
I
^
I
tV
G
li
f
i^
^'l
15
I
i
I
T6
B
I
t'V
I
"
i
.L.
=
Cutter
w C-
Shaft
V Ie "^
n
Note : Refer to table at top of page 337 for values of dimension E.
PROPORTIONS OF KEY HEADS
337
Whitney Keys and Cutters. Nos. 26 to
36
fe
>»
^
1
1
fc
5-
>.
1
^
•^fe
'o
m
^
p
oiJ
t^
m
^
6^
0
.5
^1
5TU
^1
u
.52
go
0
'So
3
15 1^
2
Q
H
^
't^
2
Q
H
i4
E
A
B
C
D
E
A
B
c
D
E
26
2i
t\
ift
*l
j\
30
3i
f
2i
if
t\
27
2i
i
III
tf
3\
31
3*
tV
2^
H
t\-
28
2Q
2i
2^
f
ifl
Iff
A
32
3i
3h
i
2|
2|
11
if
t\
R
2f
1
2tV
1
i
S3
T6
16
S
2f
t\
2t\
1
*
34
Si
f
2|
if
tV
T
2f
T6
2X>
1
i
3'>
si
H
2|
H
t\
U
V
2*
2|
2X^6
1
i
36
Si
1
2i
if
1^6
Proportions of Key Heads
(standard gage steel CO.)
'rB-^
A
B
c
D
A
B
c
D
i
i
i
3^
If
If
2i
i^
a^
tV
T^^
^\
lU
I-i
2|
iH
i
i
it
l^i
if
3
2
T^
A
1^6
lit
iH
3i
2tV
1
f
ii
-f
ll
ll
3l
2^
1^6
tV
f
-|
III
iH
3l
2t^^
^
i
^
-|
2
2
3f
2i
l\
A
^
2tV
2tV
Si
2tV
f
1
ll
-f
2i
2|
4
2i
ii
ii
IT^W
-|
2^
2A
4i
2t%
f
f
jl
f
2i
2i
4i
2|
H
+*
IfV
H
2t^
2t%
4f
2H
1
• i
I^
I
2f
2f
4i
2f
if
i^
if
itV
2t'w
2tV
4l
2H
I
I
I--
li
2h
2h
4f
2^
i^
itV
iH
ifV
2tV
2A
4l
2H
li
li
ifV
2f
2f
5
3
IT^
it\
lit
if
2H
2H
5
3T6
l|
li
2
IV^
2f
2|
5i
3^
lA
rtv
2i
I^
2H
2H
5i
3T6
If
If
2i
II^
2|
2i
Si
3i
ii^
It^
2^
If
2H
2H
5i
3i^
i|
I^
2^
Ij
3
3
5l
3l
ii^
IT^
2t
iH
338 CALIPERING AND FITTING
Table for Finding Total Keyway Depth
—La
In the column marked "Size of
Shaft" find the number representing
the size; then to the right find the
column representing the keyway to be
cut and the decimal there is the dis-
tance A, which added to the depth of
the keyway will give the total depth
from the point where the cutter first
begins to cut.
Size
of
Shaft
i
fs
1
/s
i
Keyway
Keyway
Keyway
Keyway
Keyway
^
0.0325
^
0.0289
^
0.0254
0.0413
H
0.0236
0.0379
f
0.022
0.0346
O.0511
H
0.0198
0.0314
0.0465
0.0177
0.0164
0.0283
0.0264
0.042
0.0392
0.0583
0.0544
I
0.0152
0.0246
0.0365
0.0506
0.067
ItV
0.0143
0.0228
0.0342
0.0476
0.0625
I*
0.0136
0.021
0.0319
0.0446
0.0581
IT^.-
0.0131
0.0204
0.0304
0.0421
0.0551
li
0.0127
0.0198
0.029
0.0397
0.0522
ifV
0.0123
0.0191
0.0279
0.038
0.0499
If
0.012
0.0185
0.0268
0.0364
0.0477
IT^
0.0114
0.0174
0.0254
0.0346
0.0453
I^
O.OII
0.0164
0.024
0.0328
0.0429
1T%
0.0107
0.0158
0.0231
0.0309
0.0412
I*
0.0105
0-0153
0.0221
0.0291
0.0395
iH
0.0102
0.0147
0.0214
0.0282
0.0383
If
0.0099
0.0142
0.0207
0.0274
0.0371
iH
0.0095
0.0136
0.0198
0.0265
0.0355
li
0.0093
0.013
0.019
0.0257
0.0339
l|^
0.009
0.0127
0.0184
0.025
0.0328
2
0.0088
0.0124
0.0179
0.0243
0.0317
2tV
0.0083
0.0117
0.0173
0.0236
0.0308
2i
0.0078
O.OII I
0.0168
0.0229
0.0299
2A
0.0073
0.0109
0.0163
0.0222
0.0291
2i
0.007
0.0107
0.0159
0.0216
0.0282
FINDING TOTAL KEYWAY DEPTH
Table for Finding Total Keyway Depth
339
In the column marked "Size of
Shaft" find the number representing
the size; then to the right find the
column representing the keyway to be
cut and the decimal there is the dis-
tance A, which added to the depth of
the keyway will give the total depth
from the point where the cutter first
begins to cut.
-_.LA
Size
i
i-k
f
i'b
i
of
Shaft
Keyway
Keyway
Keyway
Keyway
Keyway
2A
0.0068
0.0104
0.0155
0.0209
0.0274
2j
0.0066
0.0102
0.0152
0.0202
0.0267
2tV
0.0064
O.OI
0.0149
0.0198
0.026
2h
0.0063
0.0098
0.0146
0.0194
0.0253
2j\
0.0061
0.0094
0.0142
0.0189
0.0247
2f
0.006
0.009
0.0139
0.0185
0.0242
2H
0.0059
0.0089
0.0136
0.018
0.0236
2f
0.0058
0.0088
0.0133
0.0176
0.023
2H
0.0057
0.0086
0.0129
0.0172
0.0226
2|
0.0056
0.0084
0.0126
0.0168
0.022
2M
0.0054
0.0083
0.0122
0.0164
0.0216
3
0.0053
0.0081
0.0119
0.0161
0.0211
3t6
0.0052
0.008
0.0116
0.0158
0.0207
3i
0.0051
0.0078
0.0114
0.0155
0.0202
3^
0.005
0.0076
O.OI I 2
0.0152
0.0198
3i
0.0049
0.0075
O.OII
0.0149
0.0194
3A
0.0048
0.0074
0.0108
0.0146
O.0191
^K
0.0047
0.0072
0.0106
0.0143
0.0187
Sfe
0.0046
0.0071
0.0104
0.014
0.0184
^K
0.0045
0.007
0.0102
0.0138
0.018
3t6
0.0044
0.0069
O.OIOI
0.0135
0.0188
4.
0.0043
0.0067
O.OI
0.0133
0.0174
3H
0.0042
0.0066
0.0099
0.0131
0.0171
3l
0.0042
0.0065
0.0098
0.0128
0.0168
3H
0.0041
0.0064
0.0097
0.0126
0.0166
^l
0.0041
0.0063
0.0096
0.0124
0.0163
3il
0.0041
0.0062
0.0095
0.0123
0.0161
4
0.004
0.0061
0.0094
O.OI2I
0.016
340
CALIPERING AND FITTING
Tapers for Keys, etc., from -^^ to i inch per Foot. Amount
OF Taper for Lengths Varying by J inch
1
Length
1
I
li
2
2i
3
3i
4
4i
S
5i
6
tV
.oo';2
.0078
.0104
.0130
.0156
.0182
.0208
.0234
.0260
.0286
.0312
*
.0104
.0156
.0208
.0260
.0312
.0364
.0416
.0468
.0520
.0572
.0625
t\
.0156
.0234
.0312
.0390
.0468
.0546
.0625
.0703
.0781
.0859
•0937
i
.0208
.0312
.0416
.0520
.0625
.0729
•0833
•0937
.1041
.1145
.1250
T^^
.0260
.0390
.0520
.0650
.0781
.0911
.1041
.1171
.1302
.1432
.1562
1
.0312
.0468
.0625
.0780
•0937
.1092
.1250
.1406
.1562
.1718
•i«75
T^
.0364
.0546
.0729
.0911
•1093
•1275
.i45«
.1640
.1822
,2004
.2187
h
,0416
.0624
•0833
.1041
.1250
•1457
.1666
.1874
.2083
.2291
.2500
^
.0468
.0702
•0937
.1171
.1406
.1641
•i«75
.2109
•2343
•2577
.2812
f
.0520
.0780
.1041
.1301
.1562
.1823
.2083
•2343
.2604
.2864
•3125
ii
.0572
.0858
•I 145
•143 I
.1718
.2004
.2291
•2577
.2864
•3150
•3437
f
.0625
.0938
.1250
•1.03
•1875
.2188
•2500
•2813
•3125
•343«
•3750
H
.0677
.1016
•1354
.1693
.2031
.2370
.2708
•3047
•33«5
•3724
.4062
i
.0729
.1094
.1458
.1823
.2187
•2552
.2916
•3281
■3O45
.4010
•4375
i*
.0781
.1172
.1562
•1953
•2343
•2734
•3125
•3515
.390b
.4295
.4687
I
.0833
.1250
.1666
.2083
.2500
.2916
■3333
.3749
.4166
.45^2
.5000
1
u
1
Length
6i
7
7-^
8
8i
9
9h
10
loi
II
iii
tV
•0338
.0364
.0390
.0416
.0442
.0468
.0494
.0520
.0546
.0572
.0598
i
.0677
.0729
.0781
•0833
.088 s
•0937
.0989
.1041
.1093
.1145
.1197
A
.1015
•1093
.1171
.1250
.1328
.1406
.1484
.1562
.1640
.1718
.1796
i
■1354
.1458
.1562
.1666
.1770
•1875
.1979
.2083
.2187
.2291
•2395
1^
.1692
.1822
•1952
• 2083
•2213
•2343
•2473
.2604
•2734
.2864
.2994
^
.2031
.2187
•2343
.2500
.2656
.2812
.2968
•3125
•3281
•3437
•3593
tV
.2369
•2552
•2734
.2916
.3098
•3281
•3463
•3645
•3827
.4010
.4192
i
.2708
.2916
•3124
.3333
•3541
•3750
.3958
.4166
•4374
•4583
•4791
^
.3046
.3281
•3515
•3750
•3984
.4218
•4452
.4687
.4921
•515^
•5390
*
•3385
•3645
•3905
.4166
.4426
.4687
•4947
.5208
•5468
•5729
.5989
H
•3723
.4010
.4296
•4583
.4869
•5156
•5442
•5729
.6015
.6302
.6588
i
.4063
•4375
.4688
.5000
•5313
•5625
•5938
.6250
.6563
.6875
.7188
+*
.4401
•4739
.5078
•5416
•5755
.6093
.6432
.6770
.7109
•7447
.7786
^
•4739
•5104
•5468
•5833
.6197
.6562
.6926
.7291
•7^55
.8020
.8384
H
.5078
•5468
.5859
.6250
.6640
•7031
.7422
.7812
.8203
.8593
.8984
I
.5416
.5833
.6249
.6666
.7082
.7500
.7917
•8333
.8750
.9166
•9583
TAPERS AND DOVETAILS
MEASURING TAPERS
An Accurate Taper Gage
The gage illustrated in Fig. i is an exceedingly accurate device
for the gaging of tapers.
It is evident that if two round disks of unequal diameter are placed
on a surface plate a certain distance apart, two straight-edges touch-
It is also evident
Fig. I. — Accurate Taper Gage
that with the measuring instruments now in use it is a simple matter
to measure accurately the diameters of the two disks, and the dis-
tance these disks are apart. These three dimensions accurately and
positively determine the taper represented by the straigh .-edges
touching the rolls. If a record is made of these three dimensions
these conditions can be reproduced at any time, thus making it pos-
sible to duplicate a taper piece even though the part may not at
the time be accessible.
The formulas on the following pages may be of service in connec-
tion with a gage of this character:
341
342
TAPERS AND DOVETAILS
.///////////.//^^^^^
Taper per Foot =%
FIG. 2
Taper per Poot ■■
FIG. 3
APPLICATIONS OF FORMUt^AS 343
Formulas for Use in Connection with Taper Gage
To find Center Distance (/), refer to Fig. 2.
, R
y. + .
t
To find Disk Diameters, refer to Fig. 3.
^[Jl^+ib- ay + (& + a) I
Dia. Small Disk ^ 2 r
R
^Jl^+ib-ay- (b-aU
Dia. Large Disk = 2 R
To find Taper Per Foot (2"), refer to Fig. 4.
r = 24
Vi'-{R- ry,
To find Width of Opening at Ends, refer to Fig. 5.
Width of opening at Small End = 2 a.
\ l + (R-r)
Width of Opening at Large End = 2 b.
Applications of Formulas
To Find Center Distance Between Disks
Suppose there are two disks as shown in Fig. 2, whose diameters
are respectively ij and i inch. It is desired to construct a taper of
f to the foot and the center distance / between disks must be deter-
mined in order that the gage jaws when touching both disks shall
give that taper.
Let R = radius of large disk, or 0.625 inch.
r = radius of small disk, or 0.500 inch.
t = taper per inch on side, or
= 0.03125 mch.
24 ^ ^
344 TAPERS AND DOVETAILS
Then _ R
7^\/' + '^
3.03125 Y
000976 = 4 X 1.0005 = 4.002 inches.
To Find Disk Diameters
Suppose the gage jaws are to be set as in Fig. 3 for a three-inch
per foot taper whose length is to be four inches. The small end is
to be exactly J inch and the large end for this taper will, therefore,
be I J inches. What diameter must the disks be made so that when
the jaws are in contact with them and the distance L over the disks
measures 4 inches, the taper will be exactly three inches per foot?
Here a represents ^ the width of opening at the small end, and h one
half the width of opening at the large end. The radius of the small
disk may be found by the formula:
iW
Then
r = i{i/ L^+{b~ay+ (b-a)l.
16 + 0.25 + 0.5
= 0.0625 (4.0311 + 0.5) = 0.2832.
Diameter small disk = 0.2832 inch X 2 == 0.5664 inch.
For the large disk:
ay - (b-a)}.
16 + 0.25 - 0.5
Then
4
= 0.1875 (4-0311 - 0.5) = 0.6621.
Diameter large disk ^ 0.6621 inch X 2 = 1.3242 inches.
To Find Taper Per Foot
In duplicating a taper the gage jaws may be set to the model and
by placing between the jaws a pair of disks whose diameters are
known the taper per foot may be readily found. For example, the
jaws in Fig. 4 are set to a certain model, two disks 0.9 and i.i inch
diam.eter are placed between them and the distance over the disks
measured, from which dimension / (which is 3.5 inches) is readily
found by subtracting half the diameters of the disks. Here / repre-
sents the center distance as in Fig. 2. To determine the taper pei
foot which may be represented by T, the formula is:
^Wi'- (R-ryl
WIDTH OF GAGE OPENING 345
Then
r = 24 f "^ ] = 24 (-^] = 0.684
VV 12.25 -0.01/ \3A9^5J
Taper per foot = 0.684 inch.
To Find Width of Opening at Ends
If, with the ends of the gage jaws flush with a hne tangent to the
disk peripheries as in Fig. 5, it is required to find the width of the
opening at the small end where a represents one half that width,
the follo^ving formula may be applied, the disks being as in the last
example o.g and i.i inch diameter respectively, and the center dis-
tance 3.5 inches:
Then
0.45
11- {R
-r}
/ l+iR-
-r)
ls-S-i
•55 -
.45)
/ 3-5 + (
•55 -
•45)
0.45 \/'^ = °-45 V .94444 = .4373
0.4373 inch X 2 = 0.8746 inch width of opening at small end of gage.
Similarly the width of opening at the large end of the gage may be
found as follows, where b = half the width of the large end.
Then
V 3-4
55 - -45)
55 - 45)
■55 — 1.05882 = .56595
0-56595 inch X 2 = 1.1319 inch ^ width of opening at large end.
346
TAPERS AND DOVETAILS
BROWN & SHARPE TAPERS
347
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352
TAPERS AND DOVETAILS
k— -J— H<-
The Standard Tool Company's Standard Taper Shanks
Length
No. of
Taper
Diameter
Diameter
Total
Depth
Tongue
Thickness
Small End
Large End
Length of
Hole
to End
of
of Shank
of Shank
Shank
in Socket
Socket
Tongue
Hole
A
B
c
D
E
F
O
.2406
.3626
2H
23^2
A
3\
I
.3533
.4814
2-%
2f6
2f
?
el
2
•5531
.7099
3-
♦
J
3
• 7529
.9472
3I
3l
f^
fl •
4
.9908
1.2438
4l
4f
1
if
5
1.4390
1.7605
6|
4
f
f
6
2.0638
2.5104
8tV
7f
8
\
7
2.6849
3.2903
iif
io|
li
i|
No. of
Taper
Width
End of
Length
Diameter
Taper
Taper
of
Socket of
of
of
per
per
Keyway
Keyway
Keyway
Socket
Foot
Inch
G
H
J
: K
0
H
lit
T%
t\
.625
.05208
I
3^2
2tV
1
If
.600
.05000
il
2I
il
itV
.602
.05016
3
3tV
li
lT«
.602
.05016
4
1 -
3l
itV
IH
.623
.05191
5
h
4lf
If
2tV
.630
.05250
6
n
7
2i
2!
.626
.05216
7
l6\'
9l •
2I
.625
.05208
STANDARD TOOL COMPANY'S TAPERS
353
^ _ w///w//My//^'\
"I
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Y^'^-M^yW<y^W^
-e-
0 b'fe
The Standard Tool Company's Short Taper
No. of
Taper
Diameter
SmaU End
of Shank
Diameter
Large End
of Shank
Total
Length
of Shank
Depth
Hole
in Socket
Length
Tongue
to End
Socket
Hole
Thickness
of
Tongue
A
B
c
D
E
F
I
2
3
.378
.587
.800
.484
.706 •
.941
2\
if
\
4
1.050
1.244
3f
3
F
1
5
6
7
1-515
2.169
2.815
1.757
2.501.
3.283
4f
6f
9
3I
1
I
I
'1
No.
Width
End of
Length
Diameter
Taper
Taper
of
of
Socket to
of
of
per
per
Taper
Keyway
Keyway
Kejnvay
Socket
Foot
Inch
G
H
J
K
I
.263
If
f
II
.600
.0500
2
.388
If
I
ItV
.602
.05016
3
.520
2
li
ifV
.602
.05016
4
•645
2H
i|
^\^
.623
.05191
5
1.020
z\
2
2tV
.630
.0525
6
1.270
4f
2\
2|
.626
.05216
7
1.520
7
3
.625
.05208
THE STANDARD TOOL GO'S. SHORT TAPER SHANKS
The table shows the short taper shanks of the Standard Tool
Company for giving a tang of increased strength.
Sockets and sleeves are furnished, made with the outside taper
to fit the regular taper of spindles of drill presses; the inner taper
being suitable for the short shanks and also made with both outside
and inside taper, conforming to the new standard, and these latter
interchange or nest into each other.
354
TAPERS AND DOVETAILS
THE REED TAPER
The F, E. Reed Company, Worcester, Mass., uses in its lathe
spindles the i in 20 taper (0.6 per foot) which the Jarno system is
based on. The diameters of the Reed tapers, however, differ from
the Jarno, and the lengths in most cases are somewhat less. The
dimensions are given in the table below.
I I
F. E. Reed Lathe Center Tapers
TAPER per foot = 0.6 INCH. TAPER PER INCH = O.05 INCH
Size
of
Dia. of Small
End of
Taper
Length of
Taper
Size
of
Lathe
Dia.ofSmaU
End of
Taper
Length of
Taper
Lathe
A
B
A
B
12"
14"
16"
Special 16"
18"
1%
if
3I
4l
4h
4|
5tV
20"
22"
24''
27"
30"
li
li
If
If
2
5t\
THE JARNO TAPER
While the majority of American tool builders use the Brown &
Sharpe taper in their milling-machine spindles and the Morse taper
in their lathes, a number of firms, among them the Pratt & Whitney
Company, Hartford, Conn., and the Norton Grinding Company,
Worcester, Mass., have adopted the "Jarno" taper, the proportions
of which are given in the accompanying table. In this system the
taper of which is 0.6 inch per foot or i in 20, the number of the
taper is the key by which all the dimensions are immediately deter-
JARNO TAPERS
355
mined without the necessity even of referring to the table. That is,
the number of the taper is the number of tenths of an inch in diam-
eter at the small end, the number of eighths of an inch at the large
end, and the number of halves of an inch in length or depth. For
example: the No. 6 taper is six eighths (f) inch diameter at large
end, six tenths (j^) diameter at the small end and six halves (3
inches) in length. Similarly, the No. 16 taper is V'-, or 2 inches
diameter at the large end; }f or 1.6 inches at the small end; ^^ or
8 inches in length.
Jarno Tapers
taper per foot = 0.6 inch. taper per inch = o.05 inch.
No. of Taper
Dia. Large End
Dia. Small End =
Length of Taper
No. of Taper
10
No. of Taper
Dia. Large
Dia. Small
Length of
Dia. Large
Dia. Small
Length of
No.
End
End
Taper
No.
End
End
Taper
of
of
Taper
Taper
A
B
C
A
B
C
I
.125
.10
•5
ir
I-37S
1. 10
5-5
2
.250
.20
I-
12
1.500
1.20
6.0
3
•375
•30
1-5
13
1.625
1.30
6-5
4
.500
.40
2.0
14
1-750
1.40
7.0
5
.625
.50
2.5
15
1.875
1.50
7-5
6
•750
.60
3-0
16
2,000
1.60
8.0
7
.875
.70
3-5
17
2.125
1.70
8.5
8
1. 000
.80
4.0
18
2.250
1.80
9.0
9
1.125
.90
4.5
19
2-375
1.90
9-5
10
1.250
1. 00
5-0
20
2.500
2.00
lO.O
356
TAPERS AND DOVETAILS
-D —
Sellers Tapers
Q
t5M
II
•go
-3^
1"
II
0
fi
-ot
1
"o
•^^
SB
■5^ c
■5S
^^B
■5^^
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^f^
^^
J3
rt
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S»?^
T^Q
SO
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?,-5'c
'ix^C
.■2.S
^.£
;iJ
•^
Q
a
^
H
M
Q
J
<
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Q
?:
K
A
B
^ !
D
2A
E
F
G
H
I
K
i
i
2}
4i
6i
u
3
T6
3-7°
^\
^4
ITT
W^T
A
4i
6i
- (t
3.70
"
i
4i
7
"
<t
3-70
<(
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tV
«
Si
7i
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tt
3-70
"
((
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Si
8
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tc
=^•32
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T^6-
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6i
8
2|
i
5.32
i
ifV
fi^T
u
f
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6i
9*
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K.32
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H
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9*
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"
6.24
<c
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tt
i
«
7i
10
u
"
6.24
<c
<<
"
H
<<
7i
10
((
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6.24
"
"
"
i
i
3i
8
II*
^H
^5.-
7.28
"
"
H
"
8
iH
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i(
7.28
"
"
"
8^
12
"
9-50
"
ItV
ei
^
12
"
«
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(C
C(
il
li
li
4*
9
13*
4l
M.
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lA
9
i3i
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li
9
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"
"
ifV
9
13*
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i^
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9*
14
"
«
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<c
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ItV
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9*
14
<c
(C
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I*
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10
14*
tt
(t
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"
"
irk
10
14*
(C
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i|
If
6h
10
i6i
6f
li
tV
13-72
1
4
1V2
if
H
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10
16*
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i|
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10*
17
"
((
(C
a
«
"
i+f
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10*
17
"
(C
il
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((
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4
<c
II
17*
<(
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"
"
iH
"
II
i7i
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"
"
"
"
2
11
Hi
18
TAPER PINS AND REAMERS
357
THE SELLERS' TAPER
The system of tapers used by William Sellers & Company, Inc.,
of Philadelphia, Pa., in lathes, drilling and boring machines, is
given in the preceding table. The taper is | inch per foot and each
size of taper is splined as shown for a key the dimensions of which
are included in the table. The 'pitch of the spiral for the drills used
by the company is also included.
TAPER PINS AND REAMERS
H:
Taper Reamers and Pins
(pratt & whitney co.)
Taper = | inch per foot or .0208 inch per inch
c
1
£■31
S
0 0
of
k
Dprox. Frac-
tional Size at
Large End
of Pin
In
Q
Q
H
c75
p
<
0
0.135"
.162''
ItV
2"
28
l''
.156"
tV
I
.146''
.179''
^Tk"
2r
25
ir
.17a"
w
2
.162''
.200''
iir
2H"
19
ir
.193"
tV
3
.18 f
.226"
2^"
f
12
ir
.219"
^"
4
.208"
.257''
2r
3iV'
3
2"
.250"
r
5
.240''
.300"
2'f
4r
i
2i
.289"
6
.279"
•354''
3l"
5"
/t
3F
.341"
ii"
7
.331''
.423"
4tV'
6tV'
++
3r
.409"
w
8
.398''
.507''
.Si"
7^^
H
4r
•492"
r
9
.482-
.6og"
6r
H"
6 4
si"
.591"
-H"
10
.581''
.727"
f
9¥
6"
.706"
2 3//
II
.706''
.878"
8i"
iir
ft
7i"
■^57'
■ff"
12
.842"
1.050"
10"
i3r
If
w
I.Olf
i«V'
13
1.009"
1.259"
12"
16"
I^V
lor
1.233"
lir
These reamer sizes are so proportioned that each overlaps the
3Jze sinaller about ^ inch
358
TAPERS AND DOVETAILS
Table of Drill Sizes
FOR
Taper Pins
DrUl Sizes for Taper Pins
No.
of Pin
L
D
d
No. of
Drill
T'Ua
table
gives the drill sizes for
ine
taper
pins ranging in lengths by i 1
0.3829"
IS"
inch from No. o, f inch long, to No.
^U
0.409"
lo, 6 inches long. The diameter of
7
I 2
If"
0.409"
0.3777"
"
the small end of the pin for each
7 .
0.409"
0.3725
length
with t
is gi\
en in the fourth column
2 "
2j"
2¥'
0.409"
0.3673"
-"
le drill size in the fifth column.
0.409"
0.409"
0.3621"
0.3569"
P"
2?"
0.409"
0.3517"
s^"
3 "
3-
3-"
0.409"
0.409"
0.409"
0.3465"
0.3413"
0.3361"
1
H
~~IZI3*'
4—
— ^— i*
3-
0.409"
0.3309"
lY
1
8
li-"
0.492"
0.466 "
W
-^^j5_Length«fPinX.25
8
ir
0.492"
0.4608"
l"
8
If"
0.492"
0.4555"
§1"
8
2 "
0.492"
0.4503"
«r
8
2i"
0.492"
0.4451"
It
8
8
^}"
0.492"
0.492"
0.4399^^
f'
0.4347
No.
L
D
d
No. of
8
3
0.492"
0.4295
1%"
Pin
Drill
8
^K
0.492"
0.4243"
%%!>
8
8
§
0.492"
0.492"
0.4191
0.4139."
_xn
2Z»
o
r
0.156"
0.1404"
28
8
4 "
0.492"
. 0.4087"
J/'
o
I "
0.156"
0.1352"
29
8
4?
0.492"
0.4035
.r
I
r
0.172"
0.1564"
22
8
42"
0.492"
0.3982"
K
I
0.172"
0.1512"
24
9
1/
0.591"
0.5597"
tY
I
T-"
0.172"
0.146 "
26
9
^*:
0.591"
0.5545"
ii"
2
f"
0.193"
0.1774"
16
9
2 "
0.591"
O.S493"
II"
2
I "
0.193"
0.1722"
17
9
21"
0.591"
0.5441"
§4"
2
I-"
0.193"
0.167 "
18
9
25"
0.591"
0.5389"
ii"
2
I-"
0.193
0.1618"
20
9
2/
0.591"
0.5337"
1|"
3
_//
0.219"
0.2034"
6
9
3 "
0.591"
0.5285"
W
3
I "
0.219"
0.1982"
8
9
31"
0.591"
0.5233"
■kl"
3
I-"
0.219"
0.193 "
10
9
3r
0.591"
0.5181"
-r
3
I-"
0.219"
0.1878"
12
9
3f"
0.591"
0.5129"
%
3
I-"
0.219"
0.1825"
^4 „
9
4
0.591"
0.5077"
ir
4
-"
0.250"
0.2344"
if
9
41"
0.591"
0.5025"
4
I "
0.250"
0.2292"
Br
9
4^;
0.591"
0.4972"
1"
4
T-"
0.250"
0.224 "
I
9
4f"
0.591"
0.4929"
5"
4
li"
0.250"
0.2187"
2
9
5 "
0.591"
0.4868"
iJ"
4
if"
0.250"
0.2135"
3
9
sr
0.591"
0.4816"
K
4
2 "
0.250"
0.2083"
4
9
sr
0.591"
0.4764"
31*
5
r
0.289"
0.2734"
ii"
10
li"
0.706"
0.6747"
II"
s
0.289"
0.2682"
44"
10
If"
0.706"
0.6695"
K
5
I-"
0.289"
0.263 "
U"
10
2 "
0.706"
0.6643"
tr
s
I-"
0.289"
0.2577"
i"
10
2j"
0.706"
0.6591"
w
5
I-"
0.289"
0.2525"
4
10
2§"
0.706"
0.6539"
K
s
0.289"
0.2473"
r
10
2f"
0.706"
0.6487"
iifl
s
21"
O.2S9"
0.2421"
X5"
10
3 "
0.706"
0.643 s"
ei"
6
f"
0.341"
0.3254"
II"
10
3i"
0.706"
0.6383"
K
6
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0.341"
0.3201"
B"
10
3*"
0.706"
0.6331"
ir
6
I-"
0.341"
0.315 "
iV
10
3f"
0.706"
0.6278"
6
I-"
0.341"
0.310 "
iV
10
4 "
0.706"
0.6226"
f"
6
I-"
0.341"
0.3045"
H"
10
4-"
0.706"
0.6174"
1"
6
2 "
0.341"
0.2994"
41"
10
4-"
0.706"
0.6122"
ir
6
2-"
0.341"
0.2941"
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4 "
0.706"
0.6078"
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6
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0.341"
0.2889"
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0.706"
0.6018"
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0.2837"
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0.5966"
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0.341"
0.2785"
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0.5914"
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0.2733"
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0.706"
0.5862"
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0.409"
0.3881"
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10
6*"
0.706"
0.581 "
ORDNANCE TAPER PINS
359
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H
ij
E? I
)
c3
rt
.K
i^
g
<
H
Q
o
1
2
6
s
o
1
03
o
d
d
i
o
"t
p.
S
1
o
^
ao
"
o
H
A
^
-
to
3
36o
TAPERS AND DOVETAILS
Tapers from jL to i| inch per Foot
amount of taper for lengths up to 24 entches
Taper per Foot
•6f2
11
in
b\
i
i
f
i
f
f
I
li
V
.0002
.0002
.0003
.coo 7
.0010
.0013
.0016
.0020
.0026
.0033
tV
.0003
.0005
.0007
.0013
.0020
.0026
.0033
.0039
.0052
. .0065
i
.0007
.0010
.0013
.0026
.0039
.0052
.0065
.0078
.0104
.0130
P
.0010
.0015
.0020
.0039
.0059
.0078
.0098
.0117
.0156
.0195
i
.0013
.0020
.0026
.0052
.0078
.0104
.0130
.0136
.0208
.0260
f
.0016
.0024
.0033
.0065
.0098
.0130
.0163
.0195
.0260
.0326
t
.0020
.0029
.0039
.0078
.0117
.0156
.0195
.0234
.0312
.0391
f^
.0023
.0034
.0046
.0091
•0137
.0182
.0228
.0273
•0365
.0456
i
.0026
.0039
.0052
.0104
.0156
.0208
.0260
.0312
.0417
.0521
1^
.0029
.0044
.0059
.0117
.0176
.0234
.0293
•0352
.0469
.0586
f
•0033
.0049
.0065
.0130
.0195
.0260
.0326
.0391
.0521
.0651
ii
.0036
.0054
.0072
.0143
,0215
.0286
•0358
.0430
•0573
.0716
.0039
.0059
.0078
.0156
.0234
.0312
.0391
.0469
.0625
.0781
1^
.0042
.0063
.0085
.0169
.0254
.0339
.0423
.0508
.0677
.0846
.0046
.0068
.0091
.0182
.0273
•0365
.0456
•0547
.0729
.0911
H
.0049
.0073
.0098
.0195
.0293
.0391
.0488
.0586
.0781
.0977
I
.0052
.0078
.0104
.0208
.0312
.0417
.0521
.0625
•0833
.1042
2
.0104
.0156
.0208
.0417
.0625
.0833
.1042
.125
.1667
.2083
3
.0156
.0234
.0312
.0625
•0937
.i2c;o
.1562
•1875
.250
•3125
4
.0208
.0312
.0417
•0833
.125
.1667
.2083
.250
■3333
.4167
5
.0260
.0391
.0521
.1042
.1562
.2083
.2604
•3125
.4167
.5208
6
.0312
.0469
.0625
.125
.1875
.250
•3125
•375
.500
•625
7
•0365
•0547
.0729
.1458
.2187
.2917
.3646
•4375
.5833
.7292
8
.0417
.0625
.0833
.1667
.250
■3333
.4167
.500
.6667
•8333
9.
.0469
.0703
•0937
.1875
.2812
•375
.4687
•5625
•750
•9375
10
.0521
.0781
.1042
.2083
•3125
.4167
.5208
.625
•^333
1. 041 7
II
•0573
.0859
.1146
.2292
.3437
•4583
•5729
.6875
.9167
1.1458
12
.0625
•0937
.125
.250
•375
.500
.625
•750
1. 000
1.250
13
.0677
.1016
•1354
.2708
.4062
•5417
.6771
•8125
i^o833
1^3542
14
.0729
.1094
.1458
.2917
•4375
.5833
.7292
.875
1. 1667
1.4583
15
.0781
.1172
.1562
•3125
.4687
.625
.7812
•9375
1.250
1-5625
16
.0833
.125
.1667
■3333
.500
.6667
.8333
r.ooo
^■3333
1.6667
17
.0885
.1328
.1771
•3542'
•5312
.7083
.8854
1.0625
1.4167
1.7708
18
•0937
.1406
.1875
•3750
•5625
•750
•9375
1.125
1.500
1.875
19
.0990
.1484
.1979
•3958
•5937
.7917
.9896
1.1875
1-5833
1.9792
20
.1042
.1562
.2083
.4167
.625
.8333
1. 041 7
1.250
1.6667
2.0833
21
.1094
.1641 .2187
•4375
.6562
.875
^•0937
1^3125
i^75o
2.1875
22
.1146
.1719 .2292
.4583
.6875
.9167
1.1458
^•375
1-8333
2.2917
23
.1198
.1797
.2396
.4792
.7187
•9583
1.1970
1-4375
1.9167
2.3958
24
.125
•1875
.250
.500
•750
1. 000
1.250
1.500
2.000
2.500
TAPERS AND CORRESPONDING ANGLES 3^1
Tapers Per Foot in Inches and Corresponding Angles
Included
Angle with
Included
Angle with
*-?!
Angle
Center
Line
"S
Angle
Center .Line
s£
K^
H^
i
J
i
J
^7.
1
d
i
i
1
^^
0
4
28
0
2
14
I
4
46
18
2
23
9
3V
0
8
58
0
4
29
li
5
21
44
2
40
52
T6
0
17
54
0
8
57
il
5
57
48
2
58
54
3%
0
26
52
0
13
26
if
6
33
26
3
16
43
^
0
35
48
0
17
54
li
7
9
10
3
34
35
3\
0
44
44
0
22
22
if
7
44
48
3
52
24
A
0
53
44
0
26
52
if
8
20
26
4
10
13
/l
I
2
34
0
31
17
i|
8
56
2
4
28
I
f
I
II
36
0
35
48
2
9
31
36
4
45
48
1^
I
20
30
0
40
15
2i
10
42
42
5
21
21
I!
I
29
30
0
44
45
2j
II
53
36
5
56
48
H
I
38
22
0
49
II
2f
13
4
24
6
32
12
.^,
I
47
24
0
53
42
3
14
15
0
7
7
30
M
I
56
24
0
58
12
3i
15
25
24
7
42
42
j\
2
5
18
I
2
39
3J
16
35
40
8
17
50
¥
2
14
16
7
8
3f
17
45
40
8
52
50
^
2
23
10
II
35
4
18
55
28
9
27
44
M
2
32
4
16
2
4i
20
5
2
10
2
31
A
2
41
4
20
32
4j
21
14
2
10
37
I
if
2
50
2
25
I
4f
22
23
22
II
II
41
f
2
59
42
29
51
5
23
32
12
II
46
6
fi
3
7
56
33
58
5i
24
40
42
12
20
21
T6
3
16
54
38
27
5i
25
48
48
12
54
24
If
3-
25
50
42
55
5i
26
56
46
13
28
23
f
3
34
44
47
22
6
28
4
2
14
2
I
25
3
43
44
51
52
6i
29
II
34
14
35
47
If
3
52
38
56
19
6^-
30
18
26
15
9
13
fi
4
I
36
2
0
48
6|
31
25
2
15
42
31
i
4
10
32
2
5
16
7
32
31
12
16
15
36
II
4
19
34
'
9
47
7i
33
36
40
16
48
20
H
4
28
24
2
14
12
7^
34
42
30
17
21
15
ti
4
37
20
2
18
40
7f
35
47
32
17
53
46
8
36
52
12
18
26
6
362
TAPERS AND DOVETAILS
Table for Computing Tapers
The Tabulated Quantities = Twice the Tangent of Half the Angle.
Deg.
0'
10'
20'
30'
40'
50'
60'
0
.00000
.00290
.00582
.00872
. .01164
.01454
.01746
I
.01746
.02036
.02326
.02618
.02910
.03200
.03492
2
.03492
•03782
.04072
.04364
.04656
.04946
.05238
3
.05238
.05528
.05820
.06110
.06402
.06692
.06984
4
.06984
.07276
.07566
.07858
.08150
.08440
.08732
5
.08732
.09024
.09316
.09606
.09898
.10190
.10482
6
.10482
.10774
.11066
.11356
.11648
.11940
.12232
7
.12232
.12524
.12816
.13108
.13400
.13694
.13986
8
.13986
.14278
.14570
.14862
.15156
.15448
.15740
9
•15740
' .16034
.16326
.16618
.16912
.17204
.17498
10
.17498
.17790
.18084
.18378
.18670
.18964
.19258
II
.19258
.19552
.19846
.20138
.20432
.20726
.21020
12
.21020
.21314
.21610
.21904
.22198
.22492
.22788
13
.22788
.23082
.23376
.23672
.23966
.24262
.24556
14
.24556
.24852
.25148
.25444
.25738
.26034
.26330
15
.26330
.26626
.26922
.27218
.27516
.27S12
.28108
16
.28108
.28404
.28702
.28998
.29296
.29502
.29890
17
.29890
.30188
.30486
.30782
.31080
.31378
.31676
18
.31676
.31976
.32274
.32572
.32870
.33170
.33468
19
.33468
.33768
.34066
•34366
.34666
•34966
.35266
20
.35266
.35566
.35866
.36166
.36466
.36768
.37068
21
.37068
.37368
.37670
•37972
.38272
.38574
.38876
22
.38876
.39178
.39480
.39782
.40084
.40388
.40690
^S
.40690
.40994
.41296
.41600
.41904
.42208
.42512
24
.42512
.42816
.43120
.43424
.43728
.44034
.44338
25
.44338
.44644
.44950
.45256
.45562
.45868
.46174
26
.46174
.46480
.46786
.47094
.47400
.47708
.48016
27
.48016
.48324
.48632
.48940
.49248
.49556
.49866
28
.49866
.50174
.50484
.50794
.51004
.51414
.51724
29
.51724
.52034
•52344
.52656
.52966
.53278
.53590
30-
•53590
•53902
.54214
.54526
.54838
.55152
.55464
31
•55464
.55778
.56092
.56406
.56720
.57034
.57350
32
'5 7350
.57664
.57980
.58294
.58610
.S8926
.59242
33
,59242
.59560
.59876
.60194
.60510
.60828
.61146
34
.61146
.61464
.61782
.62102
.62420
.62740
.63060
35
63060
.63380
.63700
.64020
•64342
.64662
.64984
36
64984
.65306
.65628
•65950
.66272
.66596
.66920
37
66920
.67242
.67566
.67890
.68216
.68540
.68866
38
68866
.69192
.69516
.69844
.70170
.70496
.70824
39
70824
.71152
.71480
.71808
.72136
.72464
.72794
40
72794
.73124
.73454
•73784
.74114
.74446
•74776
41
.74776
.75108
.75440
.75774
.76106
.76440
.76772
42
.76772
.77106
.77442
.77776
.78110
.78446
.78782
43
.78782
.79118
•79454
.79792
.80130
.80468
.80806
44
.80806
.81144
.81482
.81822
.82162
.82502
.82842
45
.82842
.83184
.83526
.83866
.84210
•84552
.84894
TABLE FOR COMPUTING TAPERS
363
Table for Computing Tapers
The Tabulated Quantities = Twice the Tangent of Half the Angle.
.84894
.86962
.89046
.91146
.93262
•95396
•97546
.99716
.01906
.04114
.06342
.08592
.10862
•13154
.15470
.17810
.20172
.22560
.24974
.27414
.29882
•32378
.34902
•37456
.40042
.42658
•45308
•47992
.50710
•53466
.56258
.59088
.61956
.64868
.67820
.70816
.73858
.76946
.80080
.83266
.86504
.89792
.93138
.96540
,85238
.87308
.89394
.91496
.93616
.95752
.97906
.00080
,02272
,04484
.06716
.08968
.11242
.13538
.15858
.18202
.20568
.22960
.25378
.27824
.30296
.32796
.35326
•37984
.40476
.43098
•45754
.48442
.51168
•53928
.56726
•59562
.62440
•65356
.68316
.71320
.74368
.77464
.80608
.83802
.87048
.90346
.93700
.97112
.85582
.87656
.89744
.91848
.93970
.96110
.98268
.00444
.02638
.04854
.07090
.09346
.11624
.13924
.16248
.18594
.20966
.23362
.25784
.28234
.30710
.33216
•35750
.38314
.40910
•43538
,46200
.48894
.51624
•54392
•57196
.60040
.62922
.65846
.68814
.71824
.74882
.77984
.81138
.84340
.87594
.90902
.94266
.97686
.85926
.88002
.90094
.92202
.94326
.96468
.98630
.00808
.03006
.05226
.07464
.09724
.12006
.14310
.16636
.18988
.21362
•23764
.26190
.28644
.31126
•33636
.36176
.38744
.41346
.43980
.46646
.49348
.52084
.54856
.57668
.60516
.63406
•66338
.69312
.72332
.75396
.78506
.81668
.84878
.88142
.91458
.94832
.98262
40'
.86272
.88350
•90444
.92554
.94682
.96828
.98990
.01174
.03376
.05596
.07840
.10102
.12388
.14696
.17026
.19382
.21762
.24166
.26598
.29056
.31542
.34056
.36602
•39176
.41782
.44422
.47094
.49800
•52544
.55322
.58140
.60996
.63892
.66830
.69812
.72836
.75910
.79030
.82198
.85418
.88690
.92016
.95400
.98840
so-
.86616
.90794
.92908
•95038
.97186
■99354
.01538
.03744
.05970
.08214
.10482
.12770
.15082
.17418
.19776
.22160
•24570
.27006
.29468
.31960
•34478
.37028
.39608
.42220
.44864
•47542
■50256
.53004
•55790
.58612
.61476
.64380
.67324
•70314
.73348
.76428
•79554
.82732
.85960
.89240
.92576
.95968
.99420
•13154
•15470
.17810
.20172
.22560
.24974
.27414
.29882
•32378
•34902
•37456
.40042
.42658
.45308
.47992
.50710
.53466
.56258
.59088
.61966
.64868
.67820
.70816
.73858
.76946
.80080
.83266
.86504
.89792
.93138
.96540
2 .00000
Refer to page 364 for explanation of table.
3^4
TAPERS AND DOVETAILS
TABLE FOR USE IN COMPUTING TAPERS
In the table on pages 362 and 363 the quantities when expressed in
inches represent the taper per inch corresponding to various angles
advancing by 10 minutes from 10 minutes to go degrees. If an angle is
given as, say, 27^ degrees and it is desired to find the corresponding taper
in inches, the amount, 0.4894 may be taken directly from the table.
This is the taper per inch of length measured as in Fig. 6, along the
axis. The taper in inches per foot of length is found by multiplying
Fig. 6. — Taper per Inch and Corresponding Angle
the tabulated quantity by 12, and in this particular case would be
0.4894" X 12 = 5.8728". Where the included angle is not found
directly in the table, the taper per inch is found as follows: Assume
that the angle in question is i2j degrees, then the nearest angles in the.
table are 12° 10' and 12° 20', the respective quantities tabulated under
these angles being 0.213 14 and 0.21 610. The difference between
the two is 0.00296, and as 12^° is half way between 12° 10' and
12° 20' one half of 0.00296, or 0.00148 is added to 0.213 14, giving
0.21462" as the taper of a piece i inch in length and of an included
angle of 121 degree. The taper per foot equals 0.21362" X 12 =
2.5634".
TABLE FOR DIMENSIONING DOVETAIL SLIDES AND GIBS
The table on page 365 is figured for machine-tool work, so as to
enable one to tell at a glance the amount to be added or subtracted in
dimensioning dovetail slides and their gibs, for the usual angles up
to 60 degrees. The column for 45-degree dovetails is omitted, as A
and B would, of course, be alike for this angle.
In the application of the table, assuming a base with even dimen-
sions, as in the sketch Fig. 7, to obtain the dimensions x and y of
the slide Fig. 8, allowing for the gib which may be assumed to be
\ inch thick, the perpendicular depth of the dovetail being f inch,
and the angle 60 degrees, look under column A for f inch and it
will be found opposite this that B is 0.360 inch, which subtracted
from 2 inches gives 1.640 inches, the dimension x. To find y first
get the dimension 1.640 inches, then under the column for 6o-degree
gibs (where C is J inch), D is found to be 0.289 inch, which is added
to 1.640, giving 1,929 inches.
In practice this dimension is usually made a little larger, say to
the nearest 64th, to allow for fitting the gib.
DIMENSIONING SLIDES AND GIBS
365
I
%}i
k_B-rf w-i
Table for Dimensioning Dovetail Slides and Gibs
B
B
B
.018"
.022"
.027"
.036"
.044"
•053"
.072"
.087"
.105"
.144"
•175"
.210"
.216"
.262"
.314"
.288''
.350"
.420"
.360''
•437"
.525"
.433"
•525"
.629"
•505"
.612"
•734"
.577"
.700"
-839"
.649"
.787"
•944"
.721"
.875''
1.049"
•794"
.962"
I-I53"
.866"
1.050"
1.259"
1. 010"
1.225"
1.469"
1-154"
1.400"
1.677"
1.298"
1-575"
1.888"
1.442"
1.750"
2.097"
1.588"
1.925"
2.307"
1.732"
2.100"
2.517"
2.020"
2.450"
2.937"
2.308"
2.800"
3-356"
2.598"
3.150"
3-776"
2.885"
3-501"
4.195"
1
D
D
D
.144"
.152"
.163"
.216"
.228"
.244"
.289"
•305"
.326"
.361"
.381"
.407"
•433"
.457"
.489"
.577"
.610"
.652"
.721"
.762"
.815"
.866"
•915"
.979"
1. 010"
1.067"
1. 142"
1.154"
1.220"
1-305"
.176"
.264"
.353"
.442"
•530^
.707"
-883"
1.060"
1.237"
1. 4 1 4"
FIG. 8
366 TAPERS AND DOVETAILS
MEASURING EXTERNAL AND INTERNAL DOVETAILS
The accompanymg table of constants is for use with the plug
method of sizing dovetail gages, etc. The constants are calculated
for the plugs and angles most in use; and to use them a knowledge
of arithmetic is all that is required. The formulas by which they
were obtained are added for the convenience of those who may have
an unusual angle to make.
Fig. 9. — External and Internal Dovetails
As an example of the use of the table, suppose that Z, Fig. 9, is the
dimension wanted, and that the dimension A and the angle a are
known. A glance at the formulas above shows that Z = A — D.
Then the constant D corresponding to the size of plug and the angle
used is subtracted from A and the remainder equals Z. For instance,
ii A = 4", the plug used = f, and the angle = 30 degrees, then
Z = A-D=4''- 1.0245'' = 2.9755''.
CONSTANTS FOR DOVETAILS
^^1
If A is not known but B and C are given, according to the formula
below the table A = B -\- C F. Then if 5 = 3.134". C = J",
and the angle is 30 degrees, as before, A = B -\- C F =^ 3-134" +
{.'j^" X 1. 1547) = A"i whence Z can be found, as already shown.
If the corners of the dovetail are flat, as shown in Fig. 9 at I and
G, and the dimensions / and H and the angles are known, it will be
found from the formulas below the table that A also = I + H F;
so that if / = 3.8557", H = |", and the angle = ^o degrees, then
A = I + HF = 3.8557" + (.125" X 1. 1547) = 4^^from which Z h
found as before.
Constants for Dovetails
Plug
60°
55°
50°
45°
40°
35°
30°
r
I
I. 1830
.3170
1.0429
.3233
.9368
.3410
.8535
•3536
.7861
.3666
.7302
,3802
.6830
•3943
r
D
E
1-7745
•4755
1.5643
•4932
1.4053
.5115
1.2803
.5303
I.1792
•5499
1.0954
•5702
1.0245
•5915
¥
D
E
2.3660
.6340
2.0858
.6576
1.8730
.6820
1.7070
.7072
1.5722
•7332
1.4604
.7603
1.3660
.7886
r
D
E
3-5490
.9510
3.1286
.9864
2.S106
1.0230
2.5606
1 .0606
2.3584
1.0998
2.1903
1. 1404
2.0490
1. 1830
F
3.4641
2.8563
2.3836
2
1.67S2
1 .4004
1.1547
A = B + CF = I + HF
B=A-CF = G-HF
E = pfcot.9^±^Up
D = P [cot.
F = 2 tan a
2 ;
90 — a
+ p
368
TAPERS AND DOVETAILS
TOOL FOR LAYING OUT ANGLES ACCURATELY
The bevel gage here shown is for laying out angles accurately.
In using this gage set a vernier caliper or large "micrometer" to
twice the sine of half the angle desired, multiplied by ten, add one
m
nm
half inch and open the gage till it fits the vernier; this gives the angle
within the limits of the measuring tool and the radius of the gage.
The eighth-inch hole in the center is for a setting plug when it is
desirable to lay out an angle from a given center.
The table gives the measurements over the half disks requked for
setting the arms of the gage to give any angle from i to 45 degrees,
and also the setting for any number of holes in a circle from 3 to 22.
Table For Setting Tool For Laying Out Angles
Gage Setting For Even Degrees
Measure-
Angle
Measure-
Angle
Measure-
Angle
Measure-
Angle
ment Over
De-
ment Over
De-
ment Over
De-
ment Over
Degrees
Disks
grees
Disks
grees
Disks
grees
Disks
I
0.6746
12
2.5906
23
4.4874
34
6.3474
2
0.8490
13
2.764
24
4.6582
35
6.5142
?
1.0236
14
2.9374
25
4.8288
36
6.6804
4
1. 1980
15
3.1106
26
4.9980
37
6.846
5
1-3724
16
3-2834
27
5.1690
38
7.0114
6
1.5468
17
3-4562
28
5-3384
39
7.1762
7
1. 7210
18
3.6286
29
5-5176
40
7-3404
8
1.8952
19
3.8010
30
5-6764
41
7-5042
Q
2.0692
20
3-Q730
31
5.8448
42
7.6674
10
2.2432
21
4.1448
32
6.0128
43
7.830
II
2.4170
22
4.3162
33
6.1804
44
45
7.9922
8.1536
Gage Settings For Holes in a Circle
No. of
Holes in
Circle
Measure-
ment Over
Disks
17.8206
14.6422
12.2558
10.5
9.1776
No. of
Holes
in
Circle
Measure-
ment Over
Disks
8.1536
7-3404
6.6802
6.1346
5-6762
No. of
Holes
in
Circle
Measure-
ment Over
Disks
5.2864
4-9504
4.6582
4.4018
4-1750
No. of
Holes
Circle
Measure-
ment Over
Disks
3-9730
3-7918
3.6286
3.4808
3-3462
SHOP AND DRAWING ROOM STANDARDS
STANDARD JIG PARTS
Drill Bushings
When drilling and reaming operations are to be performed in
the same jig, two slip bushings, one for the drill and the other for
the reamer, should be used; if the jig is to be used for a large num-
ber of parts, the hole for the bushings should in turn be bushed
with a steel lining to prevent wearing. The soft cast-iron will wear
rapidly if this is not done, and the jig will soon have to be rebored
and rebushed.
«-E»3 J^--G — *j
'H-J
Fig. I
Loose Bushings
4-P
Fig. 2
Fixed Bushings
Loose Bushings
Fixed Bushings
A
B
c
D
E
G
H
A
B
C
No. 52
I
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52
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No. 30
1%
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30
16
No. 12
f
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A
tk
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ij
ii
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if
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rk
Ifv
i|
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H
ItV
i^
I
li
li
t
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i|
tV
^
li
ii
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ifV
lA
t
li
i+i
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+*
ItV
I
I
i^
li
H
i^
1 4
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I
li
I
370 SHOP AND DRAWING ROOM STANDARDS
Three different styles of bushings with their dimensions are shown
in Figs. I, 2 and 3. These can be blanked out in quantities and
finished to required sizes as needed, and should be made of tool
steel. Allowances should be made in the blanks for grinding and
A
B
c
D
E
A
B
c
D
E
^
tV
H
A
A
¥
11
ItV
1
i|
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if^
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•ft
f
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i
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32
It'6
f
i
I
i
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Fig. 3. — Fixed Bushings
lapping after hardening. Fig. i shows a slip bushing; Fig. 2 a
stationary bushing, and Fig. 3 a stationary bushing where tools with
stop collars are to be used. Such bushings as shown in Figs. 2 and
3 are also used for linings for slip bushings.
Fig. 4
Collar-Head Jig Screws.
Fig. 5
Winged Jig Screws
D
Thrd.
L
T
Ii
m
n
a:
s
D
Thrd.
H
L
T
\
20
I
f
^
x\
i
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iH
i
20
1
I
f
TG
t8
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18
'?
I
f
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t6
i^
I
^
^
f
2
5
lO
i
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14
2
i^
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^
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:|
2^
i
13
2
li
1
3^ i
Hi
JIG STRAP DIMENSIONS
371
Binding Screws
Binding- screws should be made in various sizes and with threads
to conform to the standard taps with which the shop is provided.
When drills of a very large size are used, a screw wuth a square or
hexagon head is best, as the work requires firm clamping. If the
drills used are small, a winged screw will be sufficient and more con-
venient, as it will require less time to manipulate. Some good screws
for clamping straps are sho\^ai in Figs. 4 and 5. Of course the screws
can be made of any length desired.
When the work is to be held against the seat or a stop by means
of a set-screw, such screws as shown in Figs. 6 and 7 will be found
very useful. If, however, the work is very light, a wing screw can
be used.
W
Xi
< —
-L—
1 "■
' i ' ' 1 1 1
1 '
il
D
Thrd.
L
h
I
C
H
s
D
Thrd.
L
W
d
i
20
I
I
i
/^
i
If
1
20
4
.040
A
^
18
I
T*k
i
■el
fV
ifV
■f'-Q
18
I
.057
^%
i
16
li
h
e?
1
i-i
1
16
I
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i
t'w
14
li
t'-.
r^
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14
i^
/t
*
^
13
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h
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H
i
2
i
13
li
^v
i
Fig. 6
Square- Head Jig Screws
Fig. 7
Headless Jig Screws
Supporting Screws
Figs. 8 and g show screws that are useful in supporting work against
the thrust of drills when the work is of such a nature that it cannot be
supported otherwise.
Locking Screws
A convenient hinge-cover locking screw is shown in Fig. 10. This
screw, when used, should be adjusted so that only a quarter turn will
be needed to clamp or release the cover, which should be slotted
to admit the head of the screw.
The different sizes of the styles of screws shown are not only used
with drilling jigs, but are equally useful with other jigs and fixtures.
These screws should be made of screw stock and case-hardened.
372 SHOP AND DRAWING ROOM STANDARDS
D
Thrd.
L
h
s
H
D
Thrd.
L
h
m
S
H
T
I
20
f
f
i^
^
i
20
f
A
^
li
f
^
1%
18
I
i
ih
T^
tV
18
I
^
3V
iH
I
T^
i
16
I
tV
itV
t
16
I
1^
i
iH
I
^
Fig. 8
Nurled-Head Jig Screws
Fig. 9
Nurled-Head Jig Screws
Strap Dimensions
A convenient strap to use with these jigs is shown in Fig. 11. The
straps should be made of bessemer steel and case-hardened after
finishing. The slot G can be located in the proper position and made
of such dimensions as to allow the strap lo be slipped back out of
the way when work is being placed in and taken from the jig.
111
mil?
Fig. 10. — Locking Jig Screws
Fig. II. — Jig Straps
D
Thrd.
H
h
L
S
T
W
A
B
C
D
E
L
^
18
^
t
I*
2^
l^
itV
h
I
if
i
^
2i
^
16
H
if
2A
l^
^
I
if
i
^
3
■X
14
■^
f
i|
2f
li
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1
li
2
i
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3*
i
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^
'i
ll
2I
li
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1
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2
i^
A
3^
*=
SggCTgS
t
2
4
HANDLES AND KNOBS
373
|«_._g_.^
Hdi4^
o
U
c
da
en.
w
1^
cofOfOrOfOfOPOfOfOfOCO
'Ho
OOtHHWroTj-Tj-xo vo\o
xxxxxxxxxxx
1
0000 ■^■^'^TfrJ-Tj-O OO
1 1 1 1 1 1 1 1 1 1 1
Oh
„h^H^H^H^^^^^,,«^^^
0
-t^^^^:t^^^^^^
;^
'^l^iSH«"'*"*"*'°'-HHS'«^'o*=^H2 ■
hJ
Ml(M,^r*^K5|00rHhOlOl00>O|00«H<H« " 1»
M M
U!
M M M IH M
1— »
w
MUM
0
H M M M
t*
aj;2o^«i^H« ^
w
Q
'*°"^M'frt°rr'i??^
O
hhmmmihi-imN
M
^%^^ ^ ^^r^^^^
<J
"^ r*« O M C)
fO "* ■* tOvO t^OO Ox M M M
374 SHOP AND DRAWING ROOM STANDARDS
Handles for Hand-Wheels
No.
A
B
C
D
E
F
G
H
J
P.I.
oo
i+l
it\
^1
i
t
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o
2H
lit
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M
A
^^«
28
i
2it
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-|
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si
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24
2
3t<t
2^
I
t'6
i
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24
3
3l*
2H
i^
i^
if
1
h
f
aV
24
4
4i
3i
li
i
19
f
i
t
irV
24
5
4t
3tV
A
U
tV
i
H
aV
20
6
5fV
3t
iyV
t
i
i
ii
i
aV
16
Knobs
rt
-t
->E!<
^J-;
A
B
c
D
E
F
G
H
I
J
K
tV
I
A
M
A
tV
i
i
H
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i
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A
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4-.
A
lA
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ie
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A
1
It 6
3
CO
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1
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H
^'.
1^
if
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1
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if
f
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1
BALL HANDLES
375
Ball Handles
(Pratt & Whitney Co.)
Center Ball
A
B
C
D
E
F
G
H
I
K
L
N
3
Ij6
I
f
1
3
t\
h
If
t
4
I 35
itV
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lit
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Ah
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i
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lit
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2i^
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h
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6
2h
I
it\
ifV
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i^
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7
2M
2H
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lA
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it
3ii
i
f
8
3t6
33^1
li
I^
iH
A
iiV
i
3t
il
1
K--B-^,
Binder Handles
I
1
i
c >
i< ^D >i
A
B
c
D
E
F
Dia. of Tap
i^
f
■ ::
If
If
If
2
2f
tV
f
376 SHOP AND DRAWING ROOM STANDARDS
Single End Ball Handles. (Walcott & Wood)
A
B
c
D
E
F
G
H
I
3A
4-\
i|
1
H
i
tV
^
A
3t
4-1
li
1
t*
T>
i
I
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4i
5t
if
1
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4^^
6-V
if
I
I
H
i^
1
5l
6-
rf
if
li
I
-i
f
i^
f
65
7-
2
itV
li
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6t
7-
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2
I^
lA
f
f
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8
9
^i
2i
I^
if
i
i
If
tV
Ball Lever Handles
rr
a
B
c
D
E
F
G
H
^
2|
I
If
t
H
h
if
\
.S-f
Ij
If
-*
f
A
if
1
4-
lA
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1
f
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1
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1
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f
2
7H
If
2H
I
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8-1
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I
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^
2i
HOOK BOLTS
Wing Nuts
37r
-^F
^^
A
B
c
D
E
F
R
T
tI
M
3%
^^
*i
^%
\
i
A
^TS
f
i
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A
h
1
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i
ifl
1
^ 1
t
y'b
^
i
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2A
II^
i
1
H
3\
i
i
Machine Handles
A
B
c
D
E
F
G
H
H
M
it
T^6
li^
tV
^
2|
il
if
it
fk
2
f
H
3^
si
I
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i
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2^
f
f
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it
it
t\
2H
H
H
:ff
li
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i^
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3i
1
II
ItV
iHr
. *^
, t
3i^
^
H
si
lA
^
i
A
3l
ii
li
sH
378 SHOP AND DRAWING ROOM STANDARDS
Thumb Nuts
a
'-^.^Ch^
D
A
B
c
MiU
^
7
i
3\
A
i
I
fk
*
t"^
^
li
i
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T^
'i
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3^2
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t^H
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i
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i
h
2
J%
A
i
A
f
2i
2i
1
H
tV
S^'j
1
Hook Bolts
T
L._i..
t
C I—
1
Dia. of
Thickness
•Thickness
Width
Off Set
Length
Bolt
of Head
at End
of Head
of Head
of Head
A
B
C
D
E
F
1
1^
A
f
tV
H
1
i
i
i|
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1
-^
^
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f
if
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J
H
IT%
1
-f
1^
1
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lit
I
§
I
lA
2tV
COUNTERBORES WITH INSERTED PILOTS 379
COUNTERBOEES WITH INSERTED PILOTS
ji
h __
T
)
— 1
)-
H
1
1
ill
f.
-N
i la
I--
tA— 1 I- A ":
ViXd I'Coonterbores f^ have 4 Flutes
" " 6 '^
l"to 1}^"
Diam.
A
K
L
M
N
I
i^.
\
4f
t\
7
16
i
"
*'
^\
iH
2^V
l\
5
8
ii
"
"
^
"
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Os
HI
»^
M
M
<N
CJ
CN
CN
CN
CO
0
n
to
0
to
0
to
0
^
^
to
to
so
so
t^
r^
00
^°2°S
c^ CO ^
0
0
0
M
H
M
cs
c^
N
CO CO CO
"^ ■'t
to to
so so
rO ^
CJ
CO '^
CS
CO Tj-
(S)
CO rf
CS)
CO -^
SJ S?
S S?
s:j S?
0
0
0
0 0
0
0
0
0
0
0
0
0
0
0
0
0
0
0 0
0 0
0 0
386 SHOP AND DRAWING ROOM STANDARDS
.1 •
s
i
>
1
-a
a
3
3
1
m
0 O lO O O 0
M COOO \0 t^ -T
CO CO ■* O t>- O
M
OOO
C^ CO C<
CO ^00
° ° s
M •:)- 0>
OOO
CO CO 't
eggs
O 0
§
>nO o
M M CN
V> VI O
CO C0>0
•^O O
OOO
« . CO
OOO
CO -Tio
OOO
8§
00 O
0 o o
moo
MA
OOO
CO CO ^
OOO
O OM
^82
88
8
8
to>ooo
8^^
<N <N CO
OOO
III
M H
11
CO -^
H M
O
M
O O "^ toii^ O
c»0 ■* ^ vOvO O
O 0 o
cor^ w
Hi
OOO
a.cgg
if
88
-
_c
o^.q
■* 'd- ^
q q q
o=§^
^=§^
^qq
M M M
...
M M
6
a"
...
...
. CO CO
CO CO CO
CO CO CO
COCO
3
.H
■ '■ ?
t^O CO
rr t=o
q M .
vSg
coup
. .
1
: : :
: : a,
• • •*
. 4oo o '^
iOto>0 VOVO
-a
q
.s
H 'toe
ft"?
p1 (^ fo
t-i M M
q. o
M M
1
w <S ro
Ti-u->r-
^^r?
'c?^_g^
M C0>0
CO CO CO
CO CO ^
coior^
?a
O «^>o
00 VO CO
CO ^O
B3
OO H lO
fi C^C^
O r-^ wco to
t-O -t 00 M lO
CO CO . HMO
Ovcot- M LOOv
CO 4 4 >A>oio
coOvO COOO
O 't ^ 00 00
00 t^O lO '^
rfOO n- 00 ^
tir^od 00 dv
a Q
P
_d
s
1
lO t- <M
CO CO -^
^cga
322
aja
vBR^
?s?
H
1-
3
.s
CO c^ O
CO 't CO
H OOO
HCO T
w CO lO
t^ to Tt
f^ OV M
^C lO lO lO ^ •+
CO lO t^ O M CO
fi <N cJ pi CO CO
CO CO CO
S5&
4 4
s
s •
2 m):?
I^g^
O loO
CO CO -^
too lo
O ir>0
lo O '-0
t-ooao
as8
^2
M H
s5z
M „ M
III
VO 1^00
OOO
CO 'O CO
CO CO CO
. CO '4-
CO ^ CO
CO lo CO
CO coco
M .
N N
CO CO
'1"
— /
/^^ \
s
^/'
^1
^
n
:::z
>-;c;
^
>i__
"~<^'
/>
— H
*
INTEGRAL RIGHT-ANGLED TRIANGLES
3^7
The erection of a perpendicular by the construction of a triangle
whose sides are respectively 3, 4 and 5 units in length is a familiar
and handy device. The following table gives a greater range of
choice in the shape or proportions of the triangle employed. The
table is a list of all integral, or whole-number, right-angled triangles
the units of whose least sides do not exceed 20.
Right
Base
Hypot-
enuse
Hight
Base
Hypot-
enuse
Hight
Bnse
Hypot-
enuse
3
4
5
12
16
20
17
144
195
5
12
13
12
35
37
18
24
30
6
8
10
13
84
«>
18
80
82
7
24
25
14
48
50
19
180
181
8
15
17
15
20
25
20
21
29
9
12
15
15
36
39
20
48
52
9
40
41
15
112
113
20
99
lOI
ID
24
26
16
30
34
II
60
61
16
63
65
TABLE OF CHORDS
To construct any angle from the table of chords, page 388 : Let the
required angle be 36° 38'; the nearest angles in the table are 36° 30' and
36° 40', and the chords are respectively 0.6263 and 0.6291, the differ-
ence 0.0028 corresponding to an angular difference of 10'. To find
the amount which must be added to 0.6263 (the chord corresponding
to 36° 30') in order to obtain the chord for a 36° 38' arc, multiply
0.0028 by Yo = 0.00224. 0.6263 + 0.00224 = 0.62854. Then, if the
radius is i'^ and the angle 36° 38' the chord will be 0.62854*.
In laying out an angle as in the accompanying illustration a base
line A B can be drawn, say 10 inches long, then with a radius A B
and center A, arc B C can be struck. Multiply chord 0.62854 inch
by 10 giving 6.2854 inches^ as the radius 01 an arc to be struck from
center B and cutting arc 5 C at C. Through point C draw a line
A C and the angle B A C will equal 36° 38'.
Where the angle required is in even degrees or sixths of degrees
(as to', 20', etc.) the corresponding chord may be taken directly from
the table. A 10 to i layout is particularly convenient as the multi-
plication of the tabulated chords by 10 is readily performed mentally.
SSS SHOP AND DRAWING "room STANDARDS
Table of Chords
the tabulated quantities = twice the sine of half the arc
Deg.
0'
10'
20'
30'
40'
50'
60'
o
.0000
.0029
.0058
.0087
.0116
.0145
.0174
I
.0174
.0204
•0233
.0262
.0291
.0320
.0349
2
•0349
.0378
.0407
.0436
.0465
.0494
•0523
3
.0523
•0553
.0582
.0611
.0640
.0669
.0698
4
.0698
.0727
.0756
.0785
.0814
.0843
.0872
5
.0872
.0901
.0930
•0959
.0988
.1017
.1047
6
.1047
.1076
.1105
.1134
.1163
.1192
.1221
7
.1221
.1250
.1279
.1308
■^337
.1366
.1395
8
.1395
.1424
•1453
.1482
.1511
.1540
.1569
9
.1569
.1598
.1627
.1656
.1685
.1714
-2 743
lO
.1743
.1772
.1801
.1830
.1859
.1888
.1917
II
.1917
.1946
.1975
.2004
•2033
.2062
.2090
12
.2090
.2519
.2148
.2177
.2206
•2235
.2264
13
.2264
•2293
.2322
•2351
.2380
.2409
•2437
14
•2437
.2466
.24Q5
,2524
•2553
.2582
.2610
15
.2610
.2639
.2668
.2697
.2726
•2755
•2783
i6
.2783
.2812
.2841
.2870
.2899
.2927
.2956
17
.2956
.2985
.3014
.3042
.3071
.3100
.3129
i8
.3129
•3157
.3186
•3215
•3243
.3272
•3301
19
•3301
■3330
.3358
•3387
.3416
•3444
•3473
20
•3473
.3502
•3530
•3559
•3587
.3616
•3645
21
•3645
•3673
.3702
•3730
•3759
•3788
•3816
22
.3816
•3845
.3873
.3902
•3930
•3959
•3987
23
.3987
.4016
.4044
•4073
.4101
.4130
.4158
24
.4158
.4187
.4215
.4243
.4272
.4300
.4329
25
4329
•4357
•4385
•4414
•4442
•4471
.4499
26
.4499
•4527
•4556
.4584
.4612
.4641
.4669
27
.4669
.4697
•4725
•4754
.4782
.4810
.4838
28
4838
.4867
.4895
•4923
•4951
•4979
.5008
29
.5008
•5036
.5064
.5092
.5120
.5148
•5176
30
•5176
.5204
•5232
•5261
•5289
•5317
•5345
31
•5345
•5373
.5401
•5429
•5457
•5485
•5513
32
•5513
•5541
•5569
•5596
.5624
•5652
.5680
33
.5680
.5708
•5736
•5764
•5792
.5820
•5847
34
•5847
•5875
•5903
•5931
•5959
.5986
.6014
35
.6014
.6042
.6069
.6097
.6125
•6153
.6180
36
.6180
.6208
.6236
.6263
.6291
.6318
.6346
37
.6346
•6374
.6401
.6429
.6456
.6484
.6511
38
.6511
•6539
.6566
.6594
.6621
.6649
.6676
39
.6676
.6703
.6731
.6758
.6786
.6813
.6840
40
.6840
.6868
.6895
.6922
.6950
.6977
.7004
41
.7004
•7031
•7059
.7086
•7113
.7140
.7167
42
.7167
.7194
.7222
•7249
.7276
•7303
•7330
43
•7330
•7357
.7384
.7411
•7438
•7465
.7492
44
.7492
•7519
•7546
•7573
.7600
.7627
•7654
45
.7654
.7680
.7707
•7734
.7761
•7788
•7815
CHORDS
389
Table of Chords
the tabulated quantities = twice the sine of half the arc
Deg.
0'
10'
20'
30'
40'
50'
60'
46
•7815
.7841
.7868
-7895
•7921
.7948
•7975
47
•7975
.8001
.8028
•8055
.8081
.8108
•8135
48
•8135
.8161
.8188
.8214
.8241
.8267
.8294
49
.8294
.8320
•8347
•8373
.8400
.8426
.8452
50
.8452
.8479
•8505
-8531
•8558
.8584
.8610
51
.8610
.8636
.8663
.8689
•8715
.8741
.8767
52
.8767
•8793
.8820
.8846
.8872
.8898
.8924
53
.8924
.8950
.8976
.9002
.9028
•9054
.9080
54
.9080
.9106
.9132
-9157
.9183
.9209
•9235
55
•9235
.9261
.9286
.9312
•9338
•9364
•9389
56
•9389
•9415
.9441
.9466
.9492
.9518
•9543
57
•9543
•9569
•9594
.9620
•9645 .
.9671
.9696
58
.9696
.9722
•9747
.9772
.9798
•9823
.9848
59
.9848
.9874
-9899
•9924
•9949
•9975
1 .0000
60
1 .0000
1.0025
1.0050
1.0075
1. 0100
1.0126
1.0151
61
1.0151
1.0176
1. 0201
1.0226
1. 025 1
1.0276
1. 0301
62
1. 0301
1.0326
1-0350
1-0375
1 .0400
1.0425
1.0450
63
1 .0450
I -0475
1.0500
1.0524
1-0550
1-0574
1.0598
64
1.0598
1.0623
1.0648
1.0672
1.0697
1. 072 1
1.0746
65
1.0746
1.0770
1-0795
1. 08 19
1 .0844
1.0868
1.0893
66
1.0893
1.0917
1. 094 1
1.0966
1 .0990
1.1014
1. 1039
67
I. 1039
I. 1063
1. 1087
i.iiii
I-II35
1.1159
1.1184
68
1.1184
I. 1208
1. 1232
1. 1256
1.1280
1.1304
1.1328
69
1.1328
1-1352
1. 1376
1. 1400
1. 1424
1. 1448
1.1471
70
1.1471
1.1495
1.1519
1-1543
I. 1567
1.1590
1.1614
71
1.1614.
1. 1 638
1.1661
1. 1685
1. 1708
1. 1732
1. 1756
72
1.1756'
1. 1 780
1. 1803
1. 1826
1. 1850
1.1873
1.1896
73
1.1896
1. 1920
1-1943
I. 1966
1.1990
1.2013
1.2036
74
1.2036
1.2059
1.2083
I. 2106
1.2129
1.2152
1.2175
75
1.2175
1.2198
1.2221
1.2244
1.2267
1.2290
1-2313
76
1^2313
1.2336
1.2360
1.2382
1.2405
1.2427
1.2450
77
1.2450
1-2473
1.2496
T.2518
1.2541
1.2564
1.2586
78
1.2586
1.2609
1.2631
1.2654
1.2677
1.2699
1.2721
79
1.2721
1.2744
1.2766
1.2789
1.2811
1-2833
1.2856
80
1.2856
1.2878
1.2900
1.2922
1.2945
1.2967
1.2989
81
1.2989
1. 301 1
1-3033
1-3055
1.3077
1.3099
1 .3 1 2 1
82
1.3121
1-3143
1-3165
1.3187
1.3209
1-3231
1-3252
83
1^3252
1-3274
1.3296
1-3318
1-3340
1-3361
1-3383
84
1-3383
1.3404
1.3426
1-3447
1.3469
1.3490
I-35I2
h
^•3512
^-3533
1-3555
1-3576
1-3597
1.3619
1.3640
86
1.3640
1. 3661
1.3682
1-3704
1-3725
1-3746
1-3767
87
1-3767
1.3788
1.3809
1.3030
I -385 1
1.3872
1^3893
88
^•3893
1-3914
1-3935
1-3956
1-3977
1-3997
1. 401 8
89
1.4018
1.4039
1 .4060
1 .4080
1.4101
1. 41 2 1
1. 4142
•90
1. 4142
390 SHOP AND DRAWING ROOM STANDARDS
Table for Spacing Holes in Circles
r-
Deg. of Arc
0 „
•£5
a
■an
1
-a
0 ro
•£Q
bO
C
1
■5Q
.3
r
3
120
.866
1.732
2.598
3-464
4.330
5.196
4
90
.707
1.414
2. 121
2.828
3-536
4-243
5
72
.5S8
1. 176
1.763
2-351
2.938
3-527
6
60
.500
1. 000
1.500
2.000
2.500
3.000
7
5i°-25'
.434
.868
1.302
1.736
2.170
2.604
8
45
.383
.765
1. 148
1^531
1-913
2.296
9
40
.342
.684
1.026
1.368
1. 710
2,052
lO
36
•309
.618
.927
1.236
1-545
1.854
II
32°-43'
.282
.564
.845
1. 127
1.409
1. 69 1
12
30
•259
.518
.776
1-035
1.294
1-553
13
27°-4i'
•239
•479
.718
•958
1. 197
1.436
14
25°-42'
.222
•445
.667
.890
1. 112
1-334
15
24
.208
.416
.624
•832
1.040
1.247
16
220-30'
•195
•390
•585
.780
-975
1.171
17
2I°-Il'
.184
•367
•551
•735
.918
1. 102
18
20
.174
' -347
•521
•695
.868
1. 041
19
i8°-57'
.164
•329
•493
.658
.822
.987
20
18
.156
.318
.469
.626
.782
•937
21
17°- 8'
.149
.298
•447
•596
.745
•894
22
l6°-22'
.142
.286
.427
.569
.712
•855
23
i5°-39'
.136
•273
.409
•545
.681
.818
24
15
.130
.261
•392
.522
.653
.783
25
i4°-24'
.125
.251
•375
.501
.627
•752
26
i3°-5i'
.120
.241
.361
.482
.602
•723
27
I3°-20'
.116
.232
.348
.464
•580
•697
28
I2°-5l'
.112
.224
•336
•448
.560
.672
29
I2°-25'
.108
.216
•324
.432
.540
.648
30
12
.104
.209
.314
.418
•522
.627
31
ii°-37'
.101
.202
■303
. ^404
•505
.606
32
ii°-i5'
.098
.196
•294
•393
.491
.589
SPACING HOLES IN CIRCLES
T.A3LE FOR Spacing Holes in Circles
391
90
72
60
45
40
36
32°-43'
30
27°-4i
25°-42
24
22°-30
2I°-II
20
i8°-57
18
17°- 8
l6°-2 2
i5°-39
IS
i4°-24
i3°-5i
I3°-20
I2°-5I
I2°-2 5
12
ii°-37
ii°-i5
'0
2
to
c
L
■BQ
1
1
C
1
6.062
6.928
7.794
8.660
9.526
4.950
5.657
6.364
7.071
7-778
4.II5
4.702
5.290
5.878
6.465
3.500
4.000
4.500
5.000
5-500
3.037
3-47I'
3.905
4.339
4-773
2.679
3.061
3.444
3-827
4.210
2.394
2.736
3.078
3.420
3-762
2.163
2.472
2.781
3.090
3-399
1-973
2.254
2.536
2.818
3.100
1.812
2.069
2.329
2.588
2.847
1.676
1.915
2.154
2-394
2.633
1.557
1.779
2.000
2.224
2.446
1-455
1.663
1.871
2.079
2.287
1.366
1. 561
1.756
I -951
2.146
1.286
1.469
1-653
1-837
2.020
1. 216
1.389
1.563
1-737
1.910
1.151
1.316
1.480
1.645
1.809
1.095
1.251
1.408
1.564
1.721
1 .043
1. 192
1.341
1.489
1.639
.996
I-I39
1.281
1.423
1.566
•954
1.092
1.227
1-363
1.499
.914
1.044
I.I75
1-305
1.436
.877
1.003
1.128
1-253
1-379
.843
•963
1.084
1.204
1-325
.813
•929
1.045
1. 161
1.277
.784
.896
1.008
1. 121
1-233
.756
.864
.972
1.080
1. 188
.732
.836
.941
1.045
1. 150
.707
.808
.910
1. 01 1
1. 112
.687
.785
.883
.982
1.080
392 SHOP AND DRAWING ROOM STANDARDS
TABLE FOR SPACING HOLES IN CIRCLES
The table on pages 390 and 391 will be found of service when it
is desired to space any number of holes up to and including 32, in a
circle. The number of divisions or holes desired will be found in
the first column, the corresponding angle included at the center
being given as a convenience in the second column. The remaining
column heads cover various diameters of circles from i to 12 inches,
and under these different heads and opposite the required number of
holes will be found the lengths of chords or distances between hole
centers for the given circle diameter.
Thus, if it is required to space off 18 holes in an 8-inch circle, by
following down the first column until 18 is reached and then reading
directly to the right, in the column headed "Length of Chord-
Dia. 8," will be found the distance 1.389 as the chord length for that
number of divisions and diameter of circle. Or, suppose a circle of
12 inches diameter is to be spaced off for a series of 27 holes to be
drilled at equal distances apart: Opposite 27 found in the first
column, and under the heading, "Dia, 12," will be found the chord
1.393 as the length to which the dividers may be set directly for lay-
ing off the series of holes.
If it is desired to lay off a scries of holes in a circle of some diam-
eter not given in the table, say 10 holes in an iij-inch circle, sub-
tract the chord for 10 holes in an ii-inch circle, or, 3.399 from the
chord in the "Dia. 12" column, or 3.708, and add half the difference
(.154) to 3.399, giving 3.553 as the chord or center distance between
holes. Or, if 24 holes are to be equally spaced in a 20-inch circle,
all that is necessary in order to find the chord, or center distance, is
to find opposite 24, and in the column headed, "Dia. 10," the
quantity 1.305 and multiply this by 2, giving a length of 2.610 inches
as the center distance.
TABLE OF SIDES, ANGLES AND SINES
The table on pages 393 to 397 is carried out for a much higher
number of sides or spaces than are included in the preceding table
and will be found useful in many cases not covered by that table.
It was originally computed for finding the thicknesses of commutator
bars and also for calculating the chord for spacing slots in armature
punchings. In using this table the diameter of the circle is, of
course, multij)lied by the sine opposite the desired number of holes
or sides.
Assuming for illustration that a series of 51 holes are to be equally
spaced about a circle having a diameter of 17 inches, opposite 51 in
the column headed "No. of Sides," find the quantity .06156 in. the
column headed "Sine," and multiply this quantity by 17. The
product 1.0456 is the length of the chord or the required distance
between centers of the holes for this circle. Or, if 40 equidistant
points are to be spaced about a circle 16 inches diameter, opposite
the number of sides, 40, will be found the quantity .078459 which
multiplied by 16 gives 1.255 ^ch as the distance between centers.
TABLE OF SIDES, ANGLES AND SINES 393
MULTIPLY DIAMETER BY SINE TO GET LENGTH OF SIDE
(Angle given is half of angle subtended at center)
No.
Angle
Sine
No.
Angle
Sine
Sides
Deg. Min. Sec.
Sides
Deg. Min. Sec.
• 3
60
.8660254 •
52
3-27-41.53
.060.3784
4
45
.7071067
53
3-23-46.41
.0592405
5
36
-5877852
54
3-20
.0581448
6
30
.5000000
55
3-1 6-2 1. 8 1
.0570887
7
25-42-51-42
.4338828
56
3-12-51.42
.0560704
8
22-30
.3826834
57
3- 9-28.42
.0550877
9
20-
.3420201
58
3- 6-1 2. 4 1
.0541388
lO
18-
.3090170
59
3- 3- 3-05
.0532221
II
16-21-49.09
.2817325
60
3-
.0523360
12
15-
.2588190
61
2-57- 2.95
.0514787
13
13-50-46.15
-2393157
62
2-5 4-1 1. 6 1
.0506491
14
12-51-25.71
.2225208
63
2-51-25.71
.0498458
15
12
.2079116
64
2-48- 45
.0490676
i6
11-15
.1950903
65
2-46- 9.23
•0483133
17
10-35-17-64
.1837495
66
2-43-38-18
.0475819
i8
10-
.1736481
67
2-41-11.64
.0468722
19
9-28-25.26
•1645945
68
2-38-49.41
.0461834
20
9-
-1564344
69
2-36-31-30
•0455145
21
8-34-1 7.14
.1490422
70
2-34-1 7. T4
.0448648
22
8-10-54.54
.1423148
71
2-32- 6.76
-0442333
23
7-49-33.91
.1361666
72
2-30
.0436194
24
7-30-
.1305262
73
2-27-56.71
.04302:^2
^^
7-12-
•1253332
74
2^25-56.75
.0424411
26
6-55-23-07
.1205366
75
2-24-
.041875,-
27
6-40
.1160929
76
2-22- 6.31
.0413249
28
6-25-42.85
.1119644
77
2-20-15.58
.0407885
29
6-12-24.82
.1081189
78
2-18-27.69
.0402659
30
6-
.1045284
79
2-16-42.53
•0397565
31
5-48-23.22
.1011683
80
2-15-
.0392598
32
5-37-30
.0980171
81
2-13-20
•0387753
33
5-27-16.36
.0950560
82
2-1 1-42 .45
.0383027
34
5-17-38.82
.0922683
83
2-10- 7.22
.0378414
35
5- 8-34.28
.0896392
84
2- 8-34.28
.0373911
36
5-
•0871557
85
2- 7- 3-54
.0369515
■ 37
4-51-53-51
.0848058
86
2- 5-34.88
.0365220
38
4-44-12.63
.0825793
87
2- 4- 8.27
.0361023
39
4-36-55-38
.0804665
88
2- 2-43.63
.0356923
40
4-30-
.0784591
89
2- 1-20.89
.0352914
41
4-23-24.87
.0765492
90
2-
.0348995
42
4-17- 8.57
.0747301
91
1-58-40.87
.0345160
43
4-1 1- 9.76
.0729952
92
1-57-23.47
.0341410
44
4- 5-27-27
•0713391
93
1-56- 7.74
•0337741
45
4
.0697565
94
1-54-53 -61
•0334149
46
3-54-46.95
.0682423
95
1-53-41.05
•0330633
47
3-49-47-23
.0667926
96
1-52-30.
.0327190
48
3-45-
.0654031
97
1-51-20.41
.0323818
49
3-40-24.49
.0640702
98
1-5 0-12. 24
•0320515
50
3-36-
.0627905
99
1-49- 5-45
.0317279
51
3-31-45-88
.0615609
1 100
1-48-
.0314107
394
TABLE OF SIDES, ANGLES AND SINES
MULTIPLY
DIAMETER BY SINE TO GET LENGTH OF SIDE
(Angle
given is half of angle subtended at center)
No.
Sides
Angle
Deg. Min. Sec.
Sine
No.
Sides
Angle
Deg. Min. Sec.
Sine
lOI
^.-46-5 5 -84
.0310998
151
I-II-31.39
.0208037
102
1-45-52-94
.0307950
152
I-ll- 3.15
.0206668
103
1-44-5 1. 2 6
.0304961
153
I-IO-35.29
.0205318
104
1-43-50.76
.0302029
154
I-IO- 7.79
.0203985
105
1-42-5 1. 42
.0299154
155
I- 9-40.64
.0202669
106
1-41-53-20
.0296332
156
I- 9-13.84
.0201370
107
1-40-56.07
.0293564
157
I- 8-47-38
.0200087
108
1-40-
.0290847
158
I- 8-21.26
.0198821
109
1-39- 4.95
.0288179
159
I- 7-55-47
.0197571
110
I-38-I0.90
.0285560
160
I- 7-30
.0196336
III
1-37-17-83
.0282488
161
I- 7- 4-84
.0195117
112
1-36-25. 71
.0280462
162
I- 6-40
.0193913
113
1-35-34.5 1
.0277981
163
I- 6-15.46
.6192723
114
1-34-44-21
.0275543
164
I- 5-51-21
.0191548
115
1-33-54-78
.0273147
165
I- 5-27.27
.0190387
116
'^-33- 6.20
.0270793
166
I- 5- 3-61
.0189241
117
1-32-18.46
.0268479
167
I- 4-40.23
.0188107
118
1-3 1-3 1. 5 2
.0266204
168
I- 4-17-14
.OT86988
119
1-30-45.38
.0263968
169
I- 3-54.31
.0185881
120
1-30-
.0261769
170
I- 3-31-76
.0184788
121
1-29-15-37
.0259606
171
I- 3- 9-47
.0183708
122
1-28-3 1. 47
.0257478
172
I- 2-47.44
.0182640
123
1-27-48.29
.0255386
173
I— 2-25.66
.0181584
124
1-27- 5.80
.0253326
174
I- 2- 4.13
.0180541
125
1-26-24
.0251300
175
I- 1-42.85
.0179509
126
1-25-42.85
.0249306
176
I- 1-21.81
.0178489
127
1-25- 2.36
.0247344
177
I- I- 1. 01
.0177481
128
1-24-22.50
.0245412
178
I- 0-40.44
.0176484
129
1-23-43.25
.0243509
179
I- 0-20.11
-0175498
130
1-23- 4.61
.0241637
180
I- -
.0174524
131
1-22-26.56
.0239793
181
-59-40.11
-0173559
132
I -2 1 -49 .09
.0237976
182
-59-20.43
.0172605
^33
1-21-12.18
.0236188
,183
-59- 0.98
.0171663
134
1-20-35.82
.0234425
184
-58-41.73
.0170730
135
1-20-
.0232689
185
-58-22.70
.0169807
136
1-19-24.70
.0230978
186
-58- 3-87
.0168894
137
1-18-49.92
.0229292
187
-57-45.24
.0167991
138
1-18-15.65
.0227631
188
-57-26.30
.0167097
139
1-17-41.87
.0225994
189
-57- 8.57
.0166214
140
1-17- 8.57
.0224380
190
-56-50.52
.0165339
141
1-16-35.74
.0222789
191
-56-32.67
.0164473
142
1-16- 3.38
.0221220
192
-56-15
.0163617
143
1-15-31.46
.0219673
193
-55-57-51
.0162769
144
1-15-
.0218148
194
-55-40.20
.0161930
145
1-14-28.96
.0216644
195
-55-23-07
.0161100
146
1-13-58.35
.0215160
196
-55- 6.12
.0160278
147
1-13-28.16
.0213697
197
-54-49-34
.0159464
148
1-12-58.37
.0212253
198
-54-32.72
.0158659
149
i-i 2-28.99
.0210829
199
-54-16.28
.0157862
150
1-12-
.0209424
200
-54-
.0157073
TABLE OF SIDES, ANGLES AND SINES 395
MULTIPLY DIAMETER BY SINE TO GET LENGTH OF SIDE
(Angle given is half of angle subtended at center)
No.
Sides
Angle
Min. Sec.
Sine
No.
Sides
Angle
Min. Sec.
Sine
20I
53-43-88
.0156244
251
43- 1-67
.0125160
202
53-27-92
•0155518
252
42-51.43
.0124663
203
53-12.12
•0154752
253
42-41.26
.0124171
204
52-56.47
-0153993
254
42-31.18
.0123682
205
52-40.97
.0153242
255
42-21.18
.0123197
206
52-25-63
.0152498
256
42-11.25
.0122715
207
52-10.44
.0151764
257
42- 1.40
.0122238
208
51-55-38
•0151033
258
41-51.63
.0121764
209
51-40.48
.0150310
259
41-41.93
.0121294
210
51-25-71
-0149595
260
41-32.31
.0120827
211
51-11.09
.01488S6
261
41-22.76
.0120364
212
50-56.60
.0148183
262
41-13.28
•01 1990s
213
50-42.25
.0147487
263
41- 3-88
.0119449
214
50-28.04
.0146798
264
40-54.54
.0118997
215
50-13.96
.0146115
265
40-45.28
.0118548
216
50-
.0145439
266
40-36.09
.0118102
217
49-46.17
.0144769
267
40-26.96
.0117660
218
49-32.48
.0144104
268
40-17.91
.0117221
219
49-18.91
.0143446
269
40- 8.93
.0116786
220
49- 5.46
.0142794
270
40-
.0116353
221
48-52.13
.0142148
271
39-51-14
.0115923
222
48-38.92
.0141508
272
39-42.35
.0115497
223
48-25.83
.0140874
273
39-33-63
.0115074
224
48-12.86
.0140245
274
39-24.96
.0114654
225
48-
.0139622
275
39-16.36
.0114237
226
47-47.26
.0139004
276
39- 7-83
.0113823
227
47-34.63
.0138392
277
38-59-35
.0113412
228
47-22.11
•0137785
278
38-50.94
.0113004
229
47- 9-69
.0137183
279
38-42.58
.0112599
230
46-57-39
.0136587
280
38-34.28
.0112197
231
46-45.19
•0135995
281
38-26.05
.0111798
232
46-33.10
.0135409
282
38-17.87
.0111401
233
46-2 1. 1 1
.0134828
283
38- 9-75
.0111008 •
234
46- 9-23
.0134252
284
38- 1.69
.0110617
235
45-57-45
.0133681
285
37-53-68
.0110229
236
45-45-76
•0133115
286
17-45-73
.0109844
237
45-34.18
•0132553
287
37-37-84
.0109461
238
45-22.69
.0131996
288
37-30
.0109081
239
45-11.29
.0131444
289
37-22.21
.0108704
240
45-
.0130896
290
37-14.48
^0108329
241
44-48.80
•0130353
291
37- 6.80
•0107957
242
44-37.68
.0129814
292
36-59.18
.0107587
243
44-26.67
.0129280
293
36-5 1 .60
.0107220
244
44-15-74
.0128750
294
36-44-08
.0106855
245
44- 4.90
.0128225
295
36-36.61
.0106493
246
43-54.15
.0127704
296
36-29.19
.0x06133
247
43-43-48
.0127187
297
36-21.82
.0105776
248
43-32.40
.0126674
298
36-14.50
.0105421
249
43-22.41
.0126165
299
36- 7.22
.0105068
250
43-12
.0125661
300
36-
.0104718
39^ TABLE OF SIDES, ANGLES AND SINES
MULTIPLY DIAMETER BY SINE TO GET LENGTH OF SIDE
(Angle given is half of angle subtended at center)
No.
Sides
Angle
Min. Sec.
Sine
No.'
Sides
Angle
Min. Sec.
Sine
301
35-52.82
.0104370
351
30-46.15
.0089502
302
35-45-69
. .0104024
352
30-40.91
.0089248
303
35-38.61
.0103681
353
30-35-69
.0088996
304
35-31.58
.0103340
354
30-30.51
.0088744
305
35-24.59
.0103001
355
30-25-35
.0088494
306
35-17.65
.0102665
356
30-20.22
.0088245
307
35-10.75
.0102330
357
30-15.12
.0087998
308
35- 3-90
.0101998
358
30-10.05
.0087753
309
34-57.09
.0101668
359
30- 5-01
.0087508
310
34-50.32
.0101340
360
30-
.0087265
311
34-43.60
.0101014
361
29-55.01
.0087023
312
34-36.92
.0100690
362
29-50.05
.0086783
313
34-30.29
.0100368
363
29-45.12
.0086544
314
34-23.69
.0100049
364
29-40.22
.0086306
315
34-17.14
.0099731
365
29-35-34
.0086070
316
34-TO.63
.0099415
366
29-30.49
.0085835
317
34- 4.16
.0099102
367
29-25.67
.0085601
318
33-57-74
.0098791
368
29-20.87
.0085368
319
33-51-35
.0098482
369
29-16.10
.0085137
320
33-45
.0098174
370
29-11-35
.0084907
321
33-38.69
.0097868
371
29- 6.63
.0084678
322
33-32.42
.0097564
372
29- 1.94
.0084451
323
33-26.19
.0097261
373
28-57.27
.0084224
324
33-20
.0096961
374
28-52.62
.0083999
325
33-13-85
.0096663
375
28-48
.0083775
326
33- 7-73
• .0096367
376
28-43.40
.0083552.
327
33- 1-65
.0096072
377
28-38.83
•0083331
328
32-55-61
.0095779
378
28-34.28
.0083110
329
32-49.60
.0095488
379
28-29.76
.0082891
330
32-43.64
.0095198
380
28-25.26
.0082673
33^
32-37-70
.0094911
381
28-20.78
.0082456
332
32-31.81
.0094625
382
28-16.33
.0082240
333
32-25.95
.0094341
383
28-1 1. 9 1
.0082025
334
32-20.12
.0094059
384
28- 7.50
.0081812
335
32-14.33
.0093778
385
28- 3.12
.0081599
336
32- 8.57
.0093499
386
27-58.76
.0081387
337
32- 2.85
.0093221 .
387
27-54.42
.0081177
338
31-57-16
.0092945
388
27-50.10
.0080968
339
31-51-50
.0092671
389
27-45-81
.0080760
340
31-45.88
.0092398
390
27-41.54
.0080553
341
31-40.29
.0092127
391
27-37.29
.0080347
342
31-34.74
.0091858
392
27-33.06
.0080142
343
31-29.21
.0091590
393
27-28.85
.0079938
344
31-23.72
.0091324
394
27-24.67
•0079735
345
31-18.26
.0091059
395
27-20.51
•0079533
346
31-12.83
.0090796
396
27-16.36
.0079332 •
347
31- 7-44
•0090534
397
27-12.24
.0079132
348
31- 2.07
.0090274
398
27- 8.14
•0078934
349
30-56.73
.0090016
399
27- 4.06
•0078736
350
30-51-43
.0089758
400
27-
.0078534
TABLE OF SIDES, ANGLES AND SINES
MULTIPLY DIAMETER BY SINE TO GET LENGTH OF SIDE
(Angle given is half of angle subtended at center)
397
No.
Angle
Sine
No.
Angle
Sine
Sides
Min. Sec.
Sides
451
Min. Sec.
401
26-55.96
.0078343
23-56.81
.0069658
402
26-51.94
.0078148
452
23-53.63
.0069504
403
26-47.94
.0077954
453
23-50.46
•0069351
404
26-43.96
.0077761
454
23-47-31
.0069198
405
26-40
.0077569
455
23-44.17
.0069046
406
26-36.06
.0077378
456
23-41.05
.0068894
407
26-32.14
.0077188
457
23-37-94
.0068744
408
26-28.23
.0076999
458
23-34.84
.0068594
409
26-24.35
.0076811
459
23-31.76
.0068444
410
26-20.49
.0076623
460
23-28.69
.0068295
411
26-16.64
.0076437
461
23-25.64
.0068147
412
26-12.82
.0076251
462
23-22.60
.0067999
413
26- 9.01
.0076067
463
23-19-57
.0067852
414
26- 5.22
.0075883
464
23-16.55
.0067706 ■
415
26- 1.45
.0075700
465
23-1.3-55
.0067561
416
25-57-70
.0075518
466
23-10.56
.0067416
417
25-53-96
•0075337
467
23- 7-58
.0067272
418
25-50.24
•0075157
468
23- 4.61
.0067128
419
25-46.54
•0074977
469
23- 1.66
.0066985
420
25-42.86
.0074799
470
22-58.72
.0066842
421
25-39-19
.0074621
471
22-55.79
.0066700
422
25-35-54
.0074444
472
22-52.88
.0066559
423
25-31-91
.0074268
473
22-49.98
.0066418
424
25-28.30
•0074093
474
22-47.09
.0066278
425
25-24.70
.0073919
475
22-44.21
.0066138
426
25-21.12
•0073745
476
22-41.34
•0065999
427
25-17-56
•0073573
477
22-38.49
.0065861
428
25-14.02
.0073401
478
22-35.65
.0065723
429
25-10.49
.0073230
479
22-32.82
.0065585
430
25- 6.98
•0073059
480
22-30
.0065449
431
25- 3-48
.0072890
481
22-27.20
.0065313
432
25-
.0072721
482
22-24.40
.0065178
433
24-56.54
•0072553
483
22-21.61
.0065043
434
24-53-09
.0072386
484
22-18.84
.0064909
435
24-49.66
.0072220
485
22-16.08
.0064775
436
24-46.24
.0072054
486
22-13.33
.0064641
437
24-42.84
.0071889
487
22-10.59
.0064509
438
24-39-45
.0071725
488
22- 7.87
.0064377
439
24-36.08
.0071562.
489
22- 5.16
.0064245
440
24-32.73
.0071399
490
2 2- 2.45
.0064114
441
24-29.39
.0071237
491
21-59-75
.0063983
442
24-26.06
.0071076
492
21-57.07
.0063853
443
24-22.75
.0070916
493
21-54.40
.0063723
444
24-19.46
.0070756
494
21-51.74
.0063594
445
24-16.18
-0070597
495
21-49.09
.0063466
446
24-12.91
.0070439
496
21-46.45
.0063338
447
24- 9.66
.0070281
497
21-43.82
.0063211
448
24- 6.43
.0070124
498
21-41.20
.0063084
449
24- 3.21
.0069968
499
21-38.59
.0062957
450
24-
.0069813
500
21-36
.0062831
398 SHOP AND DRAWING ROOM STANDARDS
LENGTHS OF CIRCULAR ARCS
The table gives the lengths of circular
arcs to the radius of one, for angles from
I to 1 80 degrees. The lengths for minutes of
\> arcs are given at the right.
To find the length of a circular arc with
radius of i inch and angle of 45 degrees 20
minutes. Opposite 45 degrees find 0.7854,
and opposite 20 minutes 0.0058. Adding
these gives 0.7912 inch as the length of arc.
radius is 2 inches, multiply the lengths in the table by 2.
Lengths of Circular Arcs to Radius of i
De-
gree
Length
De-
gree
45
Length
De-
gree
Length
De-
gree
Length
Min.
Length
Min.
Length
0
0.0000
0.7854
90
1-5708
135
2.3562
0
0.0000
45
0.0131
I
0.0175
46
0.8029
91
1.5882
136
2.3736
I
0.0003
46
0.0134
2
0.0349
47
0.8203
92
1.6057
137
2-3911
2
0.0006
47
0.0137
3
0.0524
48
0.8378
93
1.6232
138
2.4086
3
0.0009
48
0.0140
4
0.0698
49
0.8552
94
1.6406
139
2.4260
4
0.0012
49
0.0143
0.0873
50
0.8728
95
1.6581
140
2.4435
5
0.0015
50
0.014s
6
0.1047
51
0.8901
96
1-6755
141
2.4609
6
0.0017
51
0.0148
7
0.1222
52
0.9076
97
1-6930
142
2.4784
7
0.0020
52
0.0151
8
0.1396
53
0.9250
98
1. 7104
143
2.4958
8
0.0023
53
0.0154
9
0.1571
54
0.9425
99
1.7279
144
2.5133
9
0.0026
54
0.0157
10
0.1 745
55
0.9599
100
1-7453
145
2.5307
10
0.0029
55
0.0160
II
0.1920
56
0.9774
101
1.7628
146
2.5482
11
0.0032
56
0.0163
12
0.2094
57
0.9948
102
1.7802
147
2.5656
12
0.0035
H
0.0166
13
0.2269
58
1.0123
103
1.7977
14S
2.5831
13
0.0038
S8
0.0169
14
0.2443
59
1.0297
104
1-8151
149
2.6005
14
0.0041
59
0.0172
IS
0.2618
60
1.0472
105
1.8326
150
2.6180
15
0.0044
60
0.017s
16
0.2793
61
1.0647
106
1.8500
151
2.6354
16
0.0047
17
0.2967
62
1.0821
107
1-8675
152
2.6529
17
0.0050
18
0.3142
63
1.0996
108
1.S850
153
2.6704
18
0.0052
19
0.3316
64
1.1170
109
1.9024
154
2.6878
19
0.005 s
20
6.3491
65
I-I345
110
1.9199
155
2.7052
20
0.0058
21
0.3665
66
1.1519
111
1-9373
156
2.7227
21
0.0061
22
0.3840
67
1. 1694
112
1.9548
157
2.7402
22
0.0064
■23
0.4014
68
1. 1868
113
1.9722
158
2.7576
23
0.0067
24
0.4189
69
1.2043
114
1-9897
159
2.7751
24
0.0070
25
0.4363
70
1. 2217
115
2.0071
160
2-7925
25
0.0073
26
0.4538
71
1.2392
116
2.0246
161
2.8100
26
0.0076
27
0.4712
72
1.2566
117
2.0420
162
2.8274
27
0.0079
28
0.4887
73
1-2741
118
2-0595
163
2.8449
28
0.0081
29
0.5061
74
1.2915
119
2.0769
164
2.8623
29
0.0084
30
0.5236
75
1.3090
120
2.0944
165
2.8798
30
0.00S7
31
0.5411
76
1.3265
121
2.1118
166
2.8972
31
0.0090
32
0.5585
77
1-3439
122
2.1293
167
2.9147
32
0.0093
33
0.5760
78
1.3614
123
2.1468
i58
2.9322
33
0.0096
34
0.5934
79
r.3788
124
2.1642
169
2.9496
34
0.0099
35
0.6109
80
1-3963
125
2.1817
170
2.9671
35
0.0102
36
0.6283
8i
I-4137
126
2.1991
171
2.9845
36
0.0105
37
0.6458
82
I-4312
127
2.2166
172
3.0020
37
0.0108
38
0.6632
83
1.4486
128
2.2340
173
3-0194
38
O.OIII
39
0.6807
84
1.4661
129
2-2515
174
3-0369
39
O.OII3
40
0.6981
85
1.4835
130
2.2690
175
3-OS43
40
0.0116
41
0.7156
86
I. 5010
131
2.2864
176
3-0718
41
0.0119
42
0.7330
87
I-5184
132
2.3038
177
3-0892
42
0.0122
43
0.7505
88
1-5359
133
2.3132
178
3-1067
43
0.0125
44
0.7679
89
I-5S33
134
2.3387
179
3-1241
44
0.0128
BOLT HEAD UPSETS 399
'Actual Cutting Speed of Planers in Feet per Minute
Forward Cut-
Return Speed
ting Speed
in Feet
per Minute
2 to I
3 to I
4 to 1
5 to I
6 to I
7 to I
8 to I
20
13.3
15.
16
16.66
17.14
17-5
17.76
25
16.6
18.75
20
20.83
21.42
21.87
22.16
30
20.
22.5
24
25-
25-71
26.25
26.56
35
23-3
26.25
28
29.16
30-
30.62
31.04
40
26.6
30.
32
33-33
34-28
35-
35-52
45
30.
33-75
36
37 5
38.56
39-37
40.
50
33-3
37-5
40
41.66
42.84
43-75
44-48
55
36.6
41.25
44
45-83
47.12
48.12
48.95
60
40.
45-
48
50-
51.42
52.50
53-43
65
43-3
48.75
52
54.16
55-70
56.87
57-91
70
46.6
52.5
56
58.33
60.
61.25
62.3
75
50.
56.25
60
62.5
64.28
66.62
66.71
The table shows clearly that a slight increase in cutting speed is
better than high return speed. A 25-foot forward speed at 4 to i
return is much better than 8 to i return with 20-feet forward speed.
Economical planer speeds are given below (Cincinnati Planer Co.).
Cast Iron roughing 40 to 50 ft.; finishing 20 to 25 ft.
Steel casting and wrought iron roughing 30 to 35 ft.; finishing 20 ft.
Bronze and brass. . .50 to 60 ft.; Machinery steel. . .30 to 35 ft.
ALLOWANCES FOR BOLT HEADS AND UPSETS
Stock Allowed for Standard Upsets by Acme Machinery Co.
1 in.
Upset
to f ]
n.
Length of Up
set, 3 ir
1. Stock required, if in.
8
5
32
3 U
4
"
1
<■ ol I
32
ji 11
7 (i
((
,.1
; . I
8
l8
4
24
((
I4
a
' 4 '
. a il ,| li
li "
"
if
u
' Ah '
2\ "
T- "
ec
li
"
' Ah '
I il 11 2! "
T- "
li
if
11
5
' " " 2\ "
^ "
"
I?
u
' 5 '
2 "
li "
"
I^
5 '
' - " 2| "
5 il
. "
l|
It
' Sh '
. 11 li ^. il
3 li
a
2
11
' Sh '
i il li j| il
l| "
a
2i
a
' 6 '
2 "
2 "
"
2|
"
' 6 '
' u u ,1 11
2 "
"
2h
li
' 6 '
i il 11 i 11
2i ''
((
2t
il
' 6| '
i li 11 ,i 11
2i "
u
2!
il
' 6| '
2\ "
2i "
"
3I
"
7 '
I li "2 "
3 "
li
3i
'i
' 7 '
i il a 2I "
400 SHOP AND DRAWING ROOM STANDARDS
"x.
'.111','
1
1 ' 1 ', ' ' 1 1 1
Stock Required to Make Manufacturer's Standard Bolt
Heads and Nuts — Rough
national machinery CO.
Bolt Heads
Nuts
Square or
Hexagon
Square or Hexagon
Size Stock
Short
Stock
Required
for Upset
Short
Required
Diameter
Diameter
o
Width
Thick-
■>->
W
ness
c
1
«
Square
1
Sq.
Hexa-
gon
Sq.
Hexa-
gon
Sq.
Hexa-
gon
6
.2
P
g
Sq.
Hexa-
gon
or
Hexa-
gon
in.
in.
in.
in.
in.
in.
in.
in.
in.
in.
in.
in.
in.
1
/s
i\
• hi
§1
h
§
3^5
41
M
ii
j%
hi
^1
i
H
f
f
f
3%
li
M
M
1%
1
Tf^
a
}§
I
a
-^1
if
!l
5?
j\
U
M
1^
u
I
1
1
hi
if
ii
M
f
U
1
lA
I3='S
I
I
I'o
if
ii
U
t\
§1
U
n
13^
li
li
li
i
iiV
Il^e
hi
it
I
hi
iH
iM
li
li
1%
Ift
ii\
U
ij
Il^e
j%
if
ii%
ij
If
si
Ife
ii\
ii
lA
If
u
ll
i|
If
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§f
lie^
i/s
ii
i,^
Il%
. 1
23-^
2;^
2 ■
If
1
lit
liJ
ii^
lii
If
SI
2^
23^5
2l
2
ii
2^
lil
ii%
il
IH
it
2iS
2/s
2|
2i
1 3=^2
2t
2A
i^
2xV
2|
I^^a
33".
2§5
2|
2^
Il\
2f
2|
If
2i
2A
l|
33^.
3
3
2f
ix''.
2|
2f
If
2/h
2^
ItTij
3^1
3^
3i
3
I/.
3l
2|
i|
2f
2H
lA
3f
3M
3i
3f
Il%
3f
3l
2
2ii
2i
IM
4'3^.
3^1
3f
3i
lil
3f
3f
2|
2
3
3iV
I^
41%
4
4
3i
IH
2
3l
3f
2i
aj
3f
3^6
IJI
5
41%
4i
3f
2
2s
4i
3f
2f
2j
3f
351
l|
5f
4il
4i
4i
2i
22
4f
4l
2f
2|
4i
4i='s
2l\j
SM
5f
4f
4i
2fe
2f
4f
4f
2|
3
4i
41^6
2i
6{,
Sii
5
4f
2iJ
3
45
4f
3f
STOCK FOR BOLT HEADS AND NUTS
401
Stock Required to Make United States Standard Bolt
Heads and Nuts — Rough
NATIONAL MACHINERY CO.
Bolt Heads
Nuts
Square or Hexagon
Square or Hexagon
Size Stock
Stock Required
Required
Short
Diam-
eter
for Upset
Short
Diam-
Square or
Size
of Bolt
Thick-
ness
Diameter
Hole
Thick-
ness
Hexagon
Square
Hexa-
gon
Width
Thick-
ness
in.
in.
in.
in.
in.
*
in.
in.
in.
in.
in.
i
IT?2
ITJ^
i
r\ scant
'h
M
i\
M
M
if
It\
M
J scant
A
M
1%
H
hi
ij
li
a
U scant
§1
il
18
M
tS
If
If
M
M
7«
11
Jl
/s
i§l
li
1
if scant
ii
^1
I6
§i
li
lit
•If
Si
§1
j%
!l
M
iiV
il
2
iH
ii\
^ full
5
§J
Is
1
2 3'2
iJI
li
f scant
I?5
H
l/a
il
2|
2t.^2
l/a
li scant
If
il
If
if
2f
2f
If
§1 scant
I
Il%-
ii^
iH
§1
3
2M
lit
if fuU
ll
lA
2
I
3i
2SI
2
11^5 fuU
l8-
If
21^6
iTf^
3t%
3
2^\
13^5 full
21^6
i^
^
2|
I A
3l'e
3t%
2f
13% fuU
2\
If
2l%
13%
4tV
si
2t%
li? scant
2{,
If
2|
If
4f
3l
2f
i| scant
2f
if
2if
iM
4l
4
2if
if scant
2ii
2
3i
ii%
4f
4i
3i
lit scant
3
2f
3h
If
S/e
4§i
3i
lU scant
3f
2f
3i
iM
5il
sA
3i
2^
3f
2f
2f
4i
2i
6/e
s§
4i
2/5
2?
4^
2i
3
4i
2^
7
6i^
4f
2H
3
4i
3i
402 SHOP AND DRAWING ROOM STANDARDS
O OJ
<0 cj
-^a
tfl "p
IS =3
s
H^
3
H
-&J2
W
c o
Ph
ci
'^
5 <J
ft
Ui
^1
M
G
Q
^^
^
bX) be
U3-
cd-r:
M
^ Cj
r^;
o^
^
^S
c o
Tt
t^ r^
oT
-^^
g
c ^
8|i
dJ O
si
en
M 0) fO ^ lO t^OO O O M M r}- io>0 ^^00 O M M ro ^ \ri\0 OQ
M N CO •^ lO^O t^OO 0> O w fO •* l/^vO t^OO O O H N CO "^^O
H N rO ■^ lovo t^OO 0> O w c^ ro r)- lovO ^~'y5 O O hi N CO ■*
i-»-i M (N CO •* mvO t^OO Ov O M w <N CO Tf lOvO t^OO 0^ O
CO -"t »0 ITi'^ t-^00 <> O O
■51- lo loO r^oo O O
CO CO "* u~.\o O r^oO 0\OiOmp»cvico'+»o uivO t^OO
CO ■* '^ lOvO -O t-00 oOOvOOMC^Oico-*^ «'-!0
M M o cs coco^'+io lO'O O r^ r>-00 oo Oi 0> O O
''h MHCJlNCSCOCO"=t^lO>0 vo\0 O t^ t^ t^oo 00 0> Oi O
cococo-*^"+ioio lO^O vo MO t-- t^ r^oO
cs cocococO'^'+^'^ioio"^ lOvO
01 c< o< cocococococo
H^-Hl*rHl-*H«>0/''H|f«t-/ f^
* * * *_..*._*,
CO ^ \ri\0 t^OO Ov O
% % 6_^S ft % Sr S: ft ft ft
saqonj ui pjBoa Jo q^pjAV
WEIGHT OF FILLETS
403
QUICK WAY OF ESTIMATING LUMBER FOR A PATTERN
Multiply length, breadth, and thickness in inches together and
this by 7, pointing off three places.
Board 8 inches wide, 18 inches long, i inch thick. 8 X 18 X i
X 7 = 1.008 square feet. This is .008 too much, but near enough
for most work. Board i^ X 10 X 36 = 540 X 7 = 3.780. The
correct answer is 3.75.
Table Giving Proportionate Weight of Castings to Weight
OF Wood Patterns
A Pattern
Weighing One
Pound Made of
(Less weight of
Core Prints)
Cast
Iron
Brass
Copper
Bronze
Bell
Metal
Zinc
Pine or Fir. .
Oak
Beech
Linden
Pear
Birch
Alder
Mahogany . .
Brass
16
9
9-7
13-4
10.2
10.6
12.8
II. 7
0.85
18.8
lO.I
10.9
15.1
11.9
14-3
13.2
0.95
19.7
10.4
11.4
16.7
II. 9
12.3
14-9
13-7
0.99
19.3
10.3
II-3
15-5
11.8
12.2
14.7
13-5
0.98
17
10.9
II. 9
16.3
12.4
12.9
15-5
14.2
I.O
15.5
8.6
9.1
12.9
9.8
10.2
12.2
II. 2
0.81
Degrees Obtained by Opening a Two-Foot Rule
Degrees
Inches
Degrees
Inches
Degrees
Inches
I
.21
15
3.12
55
11.08
2
.422
20
4.17
60
12
3
.633
25
5.21
65
12.89
4
.837
30
6.21
70
13-76
5
1.04
35
7.20
75
14.61
7-5
1-57
40
8.21
80
15-43
TO
2.09
45
9.20
85
16.21
T4.5
3-015
50
10.12
90
16.97
Open a two-foot rule until open ends are distance apart given
in table when degrees given in table can be scribed. Same results
can be had with two 12-inch steel scales placed together at one end.
404 SHOP AND DRAWING ROOAI STANDARDS
WEIGHT OF FILLETS
»
To facilitate the calculations of the weights of the different parts
of a machine from the drawings, the accompanying table of areas or
volumes of fillets having radii from j^g to 3 inches can be used. It
has been calculated for fillets connecting sides that are at right angles
to each other.
Table of Areas or Volumes of Fillets
Radius of Area
or Volume
Radius of
Area or Volume
Fillet of F
illet in Sq.
Fillet
of Fillet in Sq.
in Inches or Ci
ibic Inches
in Inches
or Cubic Inches
tV
0008
It\
.5240
i
0033
^f.
.5667
A
0075
iH
.6119
i
0134
If
.6572
V
0209
Iff
.7050
1
0302
li
.7543
tV
0410
iM
.8056
h
0537
2
.8584
■h
0678
2tV
.9129
■
0838
2l •
.9690
■i
1013
2tV
1.0269
1207
2i
1.0864
•1
1417
^t\
I-I475
ll
1643
2f
1. 2105
1886
2tV
1.2749
I
2146
2i
1-3413
ItV
2423
2t%
1.4086
li
2716
2f
1.4787
lA
3026
2iJ
1-5500
li
3353
2f
1.6229
'p
3697
2}f
1.6869
if
4057
2I
1-7739
ItV -
4434
2if
1.8518
I^
4829
3
1.9314
To find the volume of a fillet by this table when the radius and
length are given, multiply the value in the table opposite the given
radius by the length of the fillet in inches, and this result multiplied
by the weight of a cubic inch of the material will give the weight of
the fillet.
USEFUL SUGGESTIONS 405
LAYING OUT A SQUARE CORNER
It sometimes happens that we wish to lay out a perfectly square
corner and have no square of any kind handy. Here is a way that
requires nothing but a scale or rule, or even a straight stick with-
out any graduations whatever will do. Using this stick, draw a
line as ^ C (Fig. i) and at one end of this draw the line B D a.t
any angle. This line must be straight, twice as long as A C and
of equal length each side of the point C Then if you join points
DAB, you have an exact right-angle or square corner.
Fig. 2 is simply another example of this, in which the line A C
has been drawn at a very different angle to show that it works in
any position. Joining the ends D A B a.s before also gives an exact
right angle.
ANOTHER METHOD
Another method is by what is known as the 6, 8 and 10 rule This
means that if a triangle has sides in the ratio of 6, 8 and 10, the angle
is 90 degrees. Lay down a line 6 units long, either inches, feet or
yards. Lay off another hne 8 units long as nearly Tight angles as
possible. Pleasure across the ends of the two lines and adjust until
this distance is 10 units, which makes it a right angle. These dis-
tances may be 3, 4 and 5; 12, 16 and 20 or any combination in this
ratio. It is largely used in laying out large corners.
SPEED FOR WOOD TURNING
A good average speed for a wood turning lathe is a surface or
cutting speed of from 1,000 to 1,500 ft. per minute. Where work
does not exceed i-in. diameter the lathe may be run 3,000 r.p.m.;
for 2-in. stock 2,500; for 3-in., 2,000, or a little less, and for larger
stock, the speed is reduced in proportion.
COOLING HOT BEARINGS
A hot box can be cooled by pouring sulphur on the bearing. It
melts at 220 degrees and puts a smooth surface on both journals
and bearings. It fills oil groove but can be dissolved with benzine
if machine cannot be stopped. Either stick or flowers of sulphur
will do. Graphite is also good but cannot be used where the color
^s objectionable as in flour mills or other white stock.
WIRE GAGES AND STOCK WEIGHTS
TWIST DRILL AND STEEL WIRE GAGE SIZES
The Twist Drill and Steel Wire Gage is used for measuring the
sizes of twist drills and steel drill rods. Rod sizes by this gage should
not be confused with Stubs' Steel Wire Gage sizes. The difference
between the sizes of corresponding numbers in the two gages ranges
from about .0005 to .004 inch, the Stubs sizes being the smaller except
in the cases of a few numbers where the systems coincide exactly.
Twist Drill and Steel Wire Gage Sizes
No.
Dia.
No.
Dia.
No.
Dia.
No.
Dia.
of
in
of
in
of
in
of
in
Gage
Inches
Gage
Inches
Gage
Inches
Gage
Inches
I
.2280
21
.1590
41
.0960
61
.0390
2
.2210
22
.1570
42
•0935
62
.0380
3
.2130
23
.1540
43
.0890
63
.0370
4
.2090
24
.1520
44
.0860
64
.0360
5
.2055
25
•1495
45
.0820
65
•0350
6
.2040
26
.1470
46
.0810
66
•0330
7
.2010
27
.1440
47
.0785
67
.0320
8
.1990
28
.1405
48
.0760
68
.0310
9
.i960
29
.1360
49
.0730
69
.02925
10
.1935
30
.1285
50
.0700
70
.0280
II
.1910
31
.1200
51
.0670
71
.0260
12
.1890
32
.1160
52
•0635
72
.0250
13
.1850
33
.1130
53
•0595
73
.0240
14
.1820
34
.1110
54
•0550
74
.0225
15
.1800
35
.1100
55
,0520
75
.0210
16
.1770
36
.1065
56
.0465
76
.0200
17
•1730
37
.1040
57
.0430
77
,0180
18
.1695
38
.1015
58
.0420
78
.0160
19
.1660
39
•0995
59
.0410
79
.0145
20
.1610
40
.0980
60
.0400
80
.0135
STUBS' GAGES
In using Stubs' Gages, the difference between the Stubs Iron Wire
Gage and the Stubs Steel Wire Gage should be kept in mind. The
Stubs Iron Wire Gage is the one commonly known as the English
Standard Wire, or Birmingham Gage, and designates the Stubs soft
wire sizes. The Stubs Steel Wire Gage is used in measuring drawn
steel wire or drill rods of Stubs' make and is also used by many
American makers of drill rods.
406
DIFFERENT STANDARDS FOR WIRE GAGES 407
DIMENSIONS IN DECIMAL PARTS OF
\N INCH
Number
American
or
Birm-
ingham
Wash-
bum &
Moen
Mfg. Co.
Trenton
Stubs'
Impe-
rial
Wire
Gage
^ U.S.
of
Brown
or Stubs'
Iron
Steel
Standard
Gage
&
Sharpe
Iron
Wire
Co.
Wire
for Plate
000000
.464
•432
.400
.46875
•4375
.40625
00000
•450
.400
0000
'^46
•454
•3938*
000
.40964
.425
•3625
.360
•372
•375
00
.3648
.380
•3310
.330
.348
•34375
0
.32486
.340
•3065
.305
.324
•3125
I
.2893
.300
.2830
.285
.227
•300
.28125
2
•25763
.284
.2625
.265
.219
.276
.265625
3
.22942
.259
•2437
.245
.212
.252
•25
4
.20431
• 238
•2253
.225
.207
.232
•234375
5
.18194
.220
.2070
.205
.204
.212
.21875
6
.16202
.203
.1920
.190
.201
.192
.203125
7
.14428
.180
.1770
•175
.199
.176
•1875
8
.12849
.165
.1620
.160
.197
.160
•171875
9
.11443
.148
.1483
.145
.194
.144
.15625
10
.10189
.134
•1350
.130
.191
.128
.140625
if
.090742
.120
.1205
.1175
.188
.116
.125
12
.080808
.109
•1055
.105
.185
.104
.109375
13
.071961
.095
.0915
.0925
.182
.092
•09375
14
.064084
.083
.0800
.080
.180
.080
.078125
15
.057068
.072
.0720
.070
.178
.072
.0703125
16
.05082
.065
.0625
.061
•175
.064
.0625
17
■045257
.058
.0540
.0525
.172
.056
.05625
18
.040303
.049
•0475
.045
.168
.048
•05
. 19
•03589
.042
.0410
.040
.164
.040
•04375
20
.031961
•035
.0348
.035
.161
.036
•0375
21
.028462
.032
.03175
.031
•157
.032
•034375
22
.025347
.028
.0286
.028
.155
.028
•03125
23
.022571
.025
.0258
.025
.153
.024
.028125
24
,.0201
.022
.0230
.0225
.151
.022
•025
25
.0179
.020
.0204
.020
.148
.020
.021875
26
.01594
.018
.0181
.018
.146
.018
.01875
27
.014195
.016
•0173
.017
.143
.0164
.0171875
28
.012641
.014
.0162
.016
.139
.0149
.015625
29
.01^257
.013
.0150
.015
.134
.0136
.0140625
30
.010025
.012
.0140
.014
.127
.0124
.0125
31
.008928
.010
.0132
.013
.120
.0116
•0109375
32
•00795
.009
.0128
.012
•115
.0108
.01015625
33
.00708
.008
.0118
.oil
.112
.0100
•009375
34
.006304
.007
.0104
.010
.110
.0092
•00859375
35
.005614
•005
•0095
.0095
.108
.0084
.0078125
36
.005
.004
.0090
.009
.106
.0076
.00703125
37
.004453
.0085
.103
.0068
.006640625
38
•003965
.008
.101
.0060
.00625
39
•003531
•0075
.099
.0052
40
•003144
.007
•097
.0048
4o8 WIRE GAGES AND STOCK WEIGHTS
Wire and Drill Sizes Arranged Consecutively
u
0
p
1
T3
S
1
w
v2
a2i
Dia. of
Wire
•Cca
2^
s
Dia. of
Wire
0.
2^
<
m
V3
H
<
pa
c
H
Gage Number
Gage Number
.00314
40
.041
58
59
•00353
39
.042
19
57
58
.00397
38
.043
57
.004
36
.045
56
• .0045
37
.0453
17
.005
36
35
.0465
56
.0056
35
.049
18
.0063
34
.050
55
.007
34
.0508
16
.0071
33
.052
55
.008 •
32
33
.055
54
54
.0089
31
.0571
15
.009
32
.058
17
53
.010
30
31
.0595
53
.0113
29
.063
• 52
.012
30
•0635
52
.0126
28
.0641
14
.013
29
80
.065
16
.0135
80
.066
51
.014
28
79
.067
51
.0142
27
.069
50
.0145
79
.070
50
.015
78
.072
13
15
49
.0159
26
•073
49
.016
27
77
78
.075
48
.0179
25
.076
48
.018
26
76
77
.077
47
.020
25
75
76
.0785
47
.0201
24
.079
46
.021
75
.0808
12
.022
24
74
.081
45
46
.0225
74
.082
45
.0226
23
.083
14
.023
73
.085
44
.024
72
73
.086
44
.025
23
72
.088
43
.0253
22
.089
43
.026
71
71
.0907
II
,027
70
.092
42
.028
22
70
•0935
42
.0285
21
•095
13
41
.029
69
.096
4t
.0293
69
.097
40
.030
68
.098
40
.031
67
68
.099
39
.032
20
21
66
67
.0995
39
•033
65
66
.101
38
.03s
20
64
65
.1015
38
•0359
19
.1019
10
.036
63
64
.103
37
.037
62
63
.104
37
.038
61
62
.106
36
•039
6o
61
.1065
36
.040
59
60
.108
35
.0403
18
WIRE AND DRILL SIZES
409
Wire and Drill Sizes Arranged Consecutively
S
1
1
w
'1
b
1
T3
^2J
Dia. of
Wire
gv5
"11
Dia. of
Wire
«c/5
li
u
i
^C/3
m
O)
H
<
pq
CO
H
Gage Number
Gage Number
.109
12
.203
6
.110
34
35
.204
5
6
•III
34
.2043
4
.112
33
.2055
5
.113
33
.207
4
.1144
9
.209
4
•115
32
.212
3
.116
32
.213
3
.120
11
31
31
.219
2
.127
30
.220
5
.1285
8
30
.221
2
.134
10
29
.227
I
.136
29
.228
X
.139
28
.2294
3
.1405
28
.234
A
.143
27
.238
4
B
.144
27
.242
C
.1443
7
.246
D
•146
26
.250
E
.147
26
.257
F
.148
9
25
.2576
2
.1495
25
.259
3
•151
24
.261
G
.152
24
.266
H
.153
23
.272
I
•154
23
.277
J
.155
22
.281
K
.157
. 21
22
.284
2
.159
21
.2893
I
.161
20
20
.290
L
.162
6
.295
M
.164
19
.300
I
.165
8
.302
N
.166
19
.316
0
.168
18
.323
P
.1695
18
.3249
0
.172
17
.332
Q
.173
17
.339
R
.175
16
.340
0
.177
16
.348
S
.178
15
.358
T
.180
7
14
15
.3648
■ 00
.1819
5
.368
u
.182
13
14
.377
V
.185
12
13
.380
00
.188
II
.386
W
.189
12
.397
X
.191
10
II
.404
Y
.1935
10
.4096
000
.194
9
.413
Z
.196
9
.4?S
000
.197'
8
.454
QOOO
.199
7
8
.469
0000
J?QI
<^
7
4IO
WIRE GAGES AND STOCK WEIGHTS
STUBS' STEEL WIRE SIZES AND WEIGHTS
As stated in the explanatory note regarding Stubs' Gages at the
bottom of page 406 the Stubs steel wire gage is used for measuring
drawn steel wire and drill rods of Stubs' make and is also used by
various drill rod makers in America.
Stubs' Steel Wire Sizes, and Weight in Pounds per Linear Foot
Letter
Dia.
Weight
No. of
Dia.
Weight
No. of
Dia.
Weight
and No.
in
per
Wire
in
per
Wire
in
per
of Gage
Inches
Foot
Gage I
nches
Foot
1
Gage
Inches
Foot
z
.413
.456
ID
191
.098
46
.079
.017
Y
.404
•437
II
1S8
•095
47
.077
.016
X
•397
.422
12
185
.092
48
•075
.015
W
.386
.399
13
182
.089
49
.072
.014
V
.377
.380
14
180
.087
50
.069
.013
u
.368
.362
15
178
•085
51
.066
.012
T
.358
.335
16
175
.082
52
.063
.Oil
s
.348
.324
17
172
.079
53
.058
.009
R
•339
•3^1
18
168
•075
54
•055
.008
Q
.332
.295
19
164
.072
55
.050
.007
p
•323
.280
20
161
.069
56
.045
.006
0
•316
.267
21
157
.066
57
.042
.0047
N
.302
• 244
22
155
.064
58
.041
.0045
M
.295
233
23
153
.063
59
.040
.0042
L
.290
.225
24
151
.061
60
.039
.0040
K
.281
.211
25
148
.059
61
.038
.0039
J
•277
.205
26
146
•057
62
•037
.0037
I
.272
.192
27
143
•055
^3
.036
•0035
H
.266
.189
28
139
.052
64
.035
.0033
G
.261
.182
29
134
.048
65
-033
.0029
F
.257
.177
30
127
• 043
66
.032
.0027
E
.250
.167
31
120
•039
67
.031
.0026
D
.246
.162
32
115
•035
68
.030
,0024
C
.242
•159
33
112
.034
69
.029
.0022
B
• 238
.152
34
IIO
.032
70
.027
.0020
A
• 234
.146
35
108
.031
71
.026
.0018
I
.227
.138
36
106
.030
72
.024
,0015
2
.219
.128-
37
.103
.028
73
.023
.0014
3
.212
.120
38
.101
.027
74
.022
.0013
4
.207
.115
39
.099
.026
75
.020
.0011
5
.204
.III
40
.097
.025
76
.018
.0009
6
.201
.108
41
•095
.024
77
.016
.0007
7
.199
.106
42
.092
.023
78
.015
,0006
8
.197
.104
43
.08S
.020
79
.014
.0005
9
.194
.101
44
45
.085
.081
.019
.018
80
•013 .
.0004
WEIGHTS OF SHEET STEEL AND IRON 41 1
Music Wire Sizes
No. of
Gage
Wash-
burn &
Moen
Webster
&
Horsefall
No. of
Gage
Wash-
burn &
Moen
Webster
&
Horsefall
No. of
Gage
Wash-
burn &
Moen
Webster
&
Horsefall
8-0
•00S3
6
.0215
.016
19
.0414
.043
7-0
.0087
7
.023
.018
20
.0434
.045
6-0
.0095
8
.0243
.020
21
.046
.047
5-0
.010
9
.0256
.022
22
.0483
.052
4-0
.Oil
.006
10
.027
.024
23
.051
•055
3-0
.012
.007
II
.0284
.026
24
•055
.059
2-0
•0133
.008
12
.0296
.029
25
.0586
.061
i-o
.0144
.009
13
.0314
.031
26
.0626
.065
I
.0156
.010
14
.0326
'O33
27
.0658
.070
2
.0166
.Oil
IS
.0345
•035
28
.072
.072
3
.0178
.012
16
.036
-037
29
.076
.077
4
.0188
.013
17
•0377
.039
30
.080
.083
5
.0202
.014
18
•0395
.041
Weights of Sheet Steel and Iron
united states standard gage
(Adopted by U. S. Government, July i, 1893)
Number
of
App.
Weight per Sq. Foot
No.
of
App.
Weight per Sq. Foot
Thickness
Thickness
Gage
Steel
Iron
Gage
Steel
Iron
0000000
•5
20.320
20.00
17
.05625
2.286
2.25
000000
.46875
19.050
18.75
18
•05
2.032
2.
00000
•4375
17.780
17-50
19
•04375
1.778
1^75
0000
.40625
16.510
16.25
20
•0375
1.524
1.50
000
•375
15.240
15.00
21
•03437
1-397
1-375
00
•34375
13.970
13-75
22
•03125
1.270
1.25
0
•3125
12.700
12.50
23
.02812
1-143
1. 125
I
.28125
11.430
11.25
24
• 025
1. 016
I.
2
.26562
10.795
10.625
25
.02187
.903
.875
3
•25
10.160
10.00
26
•01875
.762
.75
4
•23437
9-525
9-375
27
.01718
.698
.687
5
.21875
8.890
8.75
28
.01562
.635
.623
6
.20312
8.255
8.125
29
.01406
.571
.562
7
•1875
7.620
7.5
30
•0125
.508
.5
8
.17187
6.985
6.875
31
.01093
.440
.437
9
• 15625
6.350
6.25
32
.01015
.413
.406
10
.14062
5-715
5.625
33
.00937
.381
•375
II
.125
5.080
5.00
34
.00859
.349
.343
12
.10937
- 4.445
4.375
35
.00781
.317
.312
13
•09375
3.810
3-75
36
•00703
.285
.281
14
.07812
3.175
3-125
37
.00664
.271
.265
15
.07031
2.857
2.812
38
.00625
.254
.25
16
.0625
2.540
2.50
Weight of I cubic foot is assumed to be 487.7 lbs. for steel plates
and 480 lbs. for iron plates.
412
WIRE GAGES. AND STOCK WEIGHTS
Weights of Steel, Wrought Iron, Brass and Copper Plates
AMERICAN or BROWN & SHARPE GAGE
No.
Thickness
Weight in Lbs. per Square Foot
of
Gage
m
Inches
Steel
Iron
Brass
Copper
OOOO
.46
1S.77
18.40
19.688
20.838
OOO
.4096
16.71
16.38
17-533
18-557
oo
.3648
14.88
14-59
15-613
16.525
o
.3249
13.26
13.00
13.904
14.716
r
.2893
11.80
11-57
12.382
13-105
2
.2576
• IO-5I
10.30
11.027
11.670
3
.2294
9-39
9.18
9.819
10.392
4
.2043
8.34
8.17
8-745
9-255
5
.1819
7.42
7.28
7.788
8.242
6
.1620
6.61 ■
6.48
6-935
7-340
■ 7
.1443
5-89
5-77
6-175
6.536
8
.1285
5-24
5-14
5-499
5-821
9
.1144
4.67
4-58
4.898
5-183
lO
.1019
4.16
4-08
4-361
4.616
II
.0908
3-70
3-63
3.884
4.110
12
.0808
3-30
3-23
3-458
3.660
13 •
.0720
2.94
2.88
3.080
3.260
14
.0641
2.62
2.56
2-743
2.903
IS
.0571
2.33
2.28
2.442
2.585
i6
.0508
2.07
2.03
2.175
2.302
17
.0453
1.85
1.81
1-937
2-050
i8
.0403
1.64
1.61
1-725
1-825
19
•0359
1.46
1.44
1-536
1.626
20
.0320
I -3 1
1.28
1-367
1.448
21
.0285
1. 16
1. 14
1. 218
1.289
22
.0253
1.03
1. 01
1.085
1. 148
22>
.0226
.922
.904
.966
1.023
24
.0201
.820
.804
.860
.910
25
.0179
.730
.716
.766
.811
26
.0159
.649
.636
.682
.722
27
.0142
•579
.568
.608
.643
28
.0126
.514
.504
.541
.573
29
.0113
.461
•452
.482
.510
30
.0100
.408
.400
.429
.454
31
.0089
.363
.356
.382
.404
32
.0080
.326
.320
.340
.360
33
.0071
.290
.284
'0<^Z
.321
34
.0063
•257
.252
.269
.286
35
.0056
.228
.224
.240
.254
36
,0050
.190
.188
.214
.226
37
.0045
.169
.167
.191
.202
38
.0040
.151
.149
.170
.180
39
•0035
.134
.132
.151
.160
40
,0031
.119
.118
.135
.142
WEIGHTS OF SHEET METAL
413
Weights of Steel, Wrought Iron, Brass and Copper Plates
birmingham or stubs' gage
No.
of
Thickness
in
Inches
Weight in Lbs. per Square Foot
Gage
Steel
Iron
Brass
Copper
0000
.454
18.52
18.16
19.431
20.556
000
.425
17-34
17.00
18.190
19-253
00
.380
15-30
15.20
16.264
17.214
0
•340
13-87
13.60
14-552
15.402
I
.300
12.24
12.00
12.840
13-590
2
.284
11-59
11.36
12.155
12.865
3
.259
10-57
10.36
11.085
11.733
4
.238
9.71
9-52
10.186
10.781
5
.220
8.98
8.80
9.416
9.966
6
.203
8.28
8.12
8.689
9.196
7
.180
7-34
7.20
7.704
8.154
8
•165
. 6.73
6.60
7.062
7-475
9
.148
6.04
5-92
6.334
6.704
10
.134
5-47
5-36
5-735
6.070
II
.120
4.90
4.80
5-137
5-436
12
.109
4-45
4-36
4.667
4-938
13
.095
3-88
3.80
4.066
4-303
14
.083
3-39
3-32
3-552
3.769
15
.072
2.94
2.88
3.081
3.262
16
.065
2.65
2.60
2.782
2-945
17
.058
2-37
2.32
2.482
2.627
18
.049
2.00
1.96
2.097
2.220
19
.042
1. 71
1.68
1.797
1.902
20
.035
1-43
1.40
1.498
1.585
21
.032
1-31
1.28
1.369
1.450
22
.028
1. 14
1. 12
1. 198
1.270
23
.025
1.02
1. 00
1.070
1. 132
24
.022
.898
.88
.941
.997
25
.020
.816
.80
.856
.906
26
.018
.734
•72
.770
.815
27
.016
.653
.64
.685
.725
28
.014
.571
.56
.599
.634
29
.013
•530
.52
.556
.589
30
.012
.490
.48
.514
.544
31
.010
.408
.40
.428
.453
32
.009
.367
.36
.385
.408
33
.008
.326
•32
.342
.362
34
.007
.286
.28
.2996
.317.
35
.005
.204
.20
.214
.227
36
.004
.163
.16
.171
.181
414
WIRE GAGES AND STOCK WEIGHTS
Weights or Steel, Iron, Brass and Copper Wire
AMERICAN OR BROWN & SHARPE GAGE
No.
of
Gage
Dia.
in
Inches
Weight in Lbs. per iooo Linear Feet
Steel
Iron
Brass
Copper
oooo
.4600
566.03
560.74
605.18
640.51
ooo
.4096
448.88
444.68
479-91
507.95
oo
.3648
355-99
352.66
380.67
402.83
o
.3247
282.30
279.67
301.82
319-45
I
.2893
223.89
221.79
239-35
253-34
2
.2576
177-55
175-89
189.82
200.91
3
.2294
140.80
139.48
150.52
159-32
4
.2043
III. 66
110.62
119.38
126.35
5
.1819
88.548
87.720
94.666
100.20
6
.1620
70.221
69-565
75-075
79-462
7
.1447
55-685
55-165
59-545
63-013
8
.1285
44.164
43-751
47.219
49.976
9
.1144
35.026
34-699
37-437
39-636
lO
.1019
27.772
27.512
29.687
31.426
II
.0907
22.026
21.820
23-549
24.924
12
.0808
17.468
17-304
18.676
19.766
13
.0720
13-851
13.722
14.809
15-674
14
.0641
10.989
10.886
IT. 746
12.435
15
.0571
8.712
8.631
9-315
9-859
i6
.0508
6.909
. 6.845
7-587
7.819
17
•0453
5-478
5-427
5-857
6.199
i8
.0403
4-344
4.304
4-645
4.916
19
•0359
3-445
3.413
3.684
3-899
20
.0320
2.734
2.708
2.920
3-094
21
.0285
2.167
2.147
2.317
2.452
22
•0253
1. 719
1-703
1.838
1.945
23
,0226
1-363
1.350
1.457
T.542
24
.0201
1.081
1. 071
I-I55
1.223
25
.0179
.8571
.8491
.9163
.9699
26
.0159
.6797
•6734
.7267
.7692
27
.0142
•5391
.5340
.5763
.6099
28
.0126
.4275
•4235
.4570
.4837
29
.0113
.3389
.3358
.3624
.3835
30
.0100
.2688
.2663
.2874
.3042
31
,0089
.2132
.2113
.2280
.2413
32
.0080
.1691
•1675
.1808
.1913
33
.0071
.1341
.1328
.1434
.1517
34
.0063
.1063
.1053
.1137
.1204
^1
.0056
.0844
.0836
.0901
.0956
36
.0050
.0668
.0662
.0715
.0757
37
.0045
. -0530
•0525
.0567
.0600
38
.0040
.0420
.0416
.0449
.0475
39
•0035
.0333
.0330
.0356
.0375
40
.0031
.0264
.0262
.0282
.0299
WEIGHTS OF WIRE
415
Weights of Iron, Brass, and Copper Wire
birmingham or stubs' gage
Dia.
in
Inches
•454
.425
.380
.340
.300
.284
.259
.238
.220
.203
.180
.165
.148
.134
.120
.109
.095
.083
.072
.065
.058
.049
.042
.035
.032
.028
.025
.022
.020
.018
.016
.014
.013
.012
.010
.009
.008
.007
.005
.004
Weight in Lbs. per iooo Linear Feet
Iron
546.21
478.65
382.66
306.34
238.50
213-74
177-77
150.11
128.26
109.20
85.86
72.14
58-05
47-58
38.16
31-49
23.92
18.26
13-73
II. 19
8.92
6.36
4.67
3-25
2.71
2.08
1.66
1.28
1.06
.863
.680
.529
.438
.382
.266
.212
.167
•133
.066
.046
Brass
589.29
516.41
412.84
330.50
257-31
230.60
191.79
161.95
138.37
117.82
92.63
77-83
62.62
51-34
41.17
33-97
25.80
19.70
14.82
12.08
9.62
6.86
5-04
3-52
2.93
2.24
1.79
1-39
1. 14
.926
.732
.560
.483
.412
.286
.232
.183
.140
.071
.048
Copper
623.2
546.1
436.6
349-5
272.1
243-9
202.8
171-3
146.3
124.6
97.96
82.31
66.23
54.29
43-54
35-92
27.29
20.83
15-67
12.77
10.17
7-259
5-333
3-704
3.096
2.370
1.890
1.463
1.209
.979
•774
•592
.511
.435
•302
.244,
•193
.148
.075
^052
4i6
WIRE GAGES AND STOCK WEIGHTS
Weights of Steel and Iron Bars per
Linear Foot
Dia. or Dis-
Steel |
Iron
tance Across
Weight
per Foot
Weight per Foot
Flats
Round
Square
Hexagon
Octagon
Round
Square
^
• OIO
.013
.012
.Oil
.010
.013
i
.042
.053
.046
.044
.041
.052
t\
.094
.119
.103
.099
.092
.117
i
.167
.212
.185
.177
.164
.208
A
.261
•333
.288
.277
.256
•326
1
•375
.478
.414
.398
.368
.469
^
•511
.651
.564
•542
•501
•638
h
.667
.850
•737
.708
•654
•833
t\
.845
1.076
.932
.896
.828
1.055
1
1-043
1.328
1. 151
1. 107
1.023
1.302
ii
1.262
1.608
1.393
I.33I
1.237
1.576
i
1.502
1.913
1.658
1.584
1.473
1.875
H
1.763
2.245
1.944
1.860
1.728
2.201
1
2.044
2.603
2.256
2.156
2.004
2.552
il
2.347
2.989
2.591
2.482
2.301
2.930
I
2.670
3.400
2.947
2.817
2.618
3-333
itV
3.014
3.838
3'327
3.182
2.955
3.763
li
3.379
4.303
3.730
3.568
3-3^3
4.219
it\
3.766
4.795
4.156
3.977
3.692
4.701
li
4.173
5.312
4.605
4.407
4.091
5.208
lA
4.600
5.857
5.077
4.858
4.510
5.742
If
5-049
6.428
5.571
5.331
4.950
6.^02
itV
5.518
7.026
6.091
5.827
5.410
6.888
I^
6.008
7.650
6.631
6.344
5.890
7.500
IT^6
6.520
8.301
7.195
6.905
6.392
8.138
if
7.051
8.978
7.776
7.446
6.913
8.802
iH
7.604
9.682
8.392
8.027
7.455
9.492
If
8.178
10.41
9.025
8.635
8.018
10.21
iH
8.773
II. 17
9.682
9.264
8.601
10.95
i|
9.388
11.95
10.36
9.918
9.204
11.72
lit
10.02
12.76
11.06
10.58
9.828
12.51
2
10.68
13.60
11.79
11.28
10.47
13.33
2|
12.06
15.35
13.31
12.71
11.82
15.05
2?
13.52
17.22
14.92
14.24
13.25
16.88
2|
15.07
19.18
16.62
15.88
14.77
18.80
2h
16.69
21.25
18.42
17.65
16.36
20.83
2f
18.40
23.43
20.31
19.45
18.04
22.97
2|
20.20
25.71
22.29
21.28
19.80
25.21
2|
22.07
2S.10
24.36
23.28
21.64
27.55
3
24.03
30.60
26.53
25.36
23.56
30.00
3i
26.08
33.20
28.78
27.50
25.57
32.55
3i
28.20
35.92
31.10
29.28
27.65
35.21
3l
30.42
38.78
33.57
32.10
29.82
37-97
3^
32.71
41.65
36.10
34.56
32.07
40.83
3f
35.09
44.68
38.73
37.05
34.40
43.80
3f
37.56
47.82-
41.45
39.68
36.82
46.88
3l
40.10
51.05
44.26
42.35
39.31
50.05
4
42.73
54.40
47.16
45.12
41.89
53-33
WEIGHTS OF BAR STOCK
417
Weights of Brass, Copper and
Aluminum Bars
PER Linear Foot
Dia. or
Brass
Copper
Aluminum
Dis-
tance
Across
Flats
Weight per Foot
Weight
per Foot
Weight
per Foot
Round
Square
Hexagon
•Round
Square
Round
Square
tV
.oil
.014
.013
.012
.015
.003
.004
k
.045
.055
.048
.047
.060
.014
.018
t\
.100
•125
.108
.106
•135
.032
.041
i
•175
.225
.194
.189
.241
.057
.072
t\
•275
•350
.301
.296
•377
.089
.114
t
•395
.510
.436
.426
.542
.128
.163
t\
.540
.690
.592
.579
•737
.174
.222
^
.710
.905
.773
•757
•964
.227
.290
t\
.900
I-I5
.978
.958
1.22
.288
.367
f
1. 10
1.40
1.24
1. 18
1-51
.356
•453
u
'•^1
1.72
1-45
1-43
1.82
.430
.548
f
1.66
2.05
1-73
1.70
2.17
.516
.652
if
1.85
2.40
2.03
2.00
2.54
.601
.766
7
1"
2.15
2-75
2.36
2.32
2-95
.697
.888
H
2.48
3-15
2.71
2.66
3-39
.800
1.02
I
2.8s
3-65
3.10
3-03
3.86
.911
1. 16
itV
3.20
4.08
3-49
3-42
4-35
1.03
I-3I
li
3-57
4-55
3-91
3.81
4.88
I-I5
1.47
lA
3-97
5.08
4-38
4.27
5-44
1.28
1.64
li
4.41
5-65
4.82
4.72
6.01
1.42
1.81
lA
4.86
6.22
5-33
5-21
6.63
1-57
2.00
if
5-35
6.81
5-76
5-72
7.24
1.72
2.19
ItV
5.86
7-45
6.38
6.26
7-97
1.88
2.40
ih
6.37
8.13
6.92
6.81
8.67
2.05
2.61
iys
6.92
8.83
7-54
7-39
9.41
2.22
2.83
if
7.48
9-55
8.15
7-99
10.18
2.41
3.06
IH
8.05
10.27
8.80
8.45
10.73
2.59
•3-30
if
8.65
11.00
9-47
9.27
11.80
2.79
3-55
iH
9.29
11.82
10.15
9.76
12.43
2.99
3.81
ll
9-95
12.68
10.86
10.64
13-55
3-20
4.08
iM
10.58
13-50
11.68
II. II
14-15
3-41
4-35
2
11.25
14-35
12.36
12. II
15.42
3-64
4-64
2i
12.78
16.27
13.92
13-67
17.42
4.11
5-24
2i
14.32
18.24
15-72
15-33
19-51
4.61
5-87
2|
15.96
20.32
17-52
17.08
21.74
5-14
6.54
2^
17.68
22.53
19.44
18.92
24.09
5-69
7-25
2f
19-50
24-83
21.24
20.86
26.56
6.27
7-99
2f
21.40
27-25
23-40
22.89
29.05
6.89
8.53
2|
23-39
29-78
25.82
25.02
31.86
7-52
9-58
3
25-47
32-43
27.84
27.24
34-69
8.20
10.44
3i
30-45
38.77
32.76
31-97
40.71
9.62
12.25
3^
35-31
44-96
37-80
37-08
47.22
II. 16
14.21
3f
40.07
51.01
43-56
42.11
53-61
/2.81
16.31
4
46.12
58-73
49-44
48.43
61.67
14.56
18.56
4i8
WIRE GAGES AND STOCK WEIGHTS
vO
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■*» °^i:^ "*« ^H "H- "1:^ -^ ::^
r-i|ao ihHi Hn
M M M H
WEIGHTS OF SEAMLESS BRASS TUBING
419
1
ro 0 CO M 0 0
10 ICO M Th 0 rOOO 0 00 VO 0 r^OO M TtOO Tt t-. OS n M rfO m
r-- '^ On up M 00 CO OvO C| On !>. ro q 00 MD rt CS q 00 00 r^O lO to
\OOiOlOtO'^'rl-rorOco<NC^pi(NMMMMiH
-
<>.00 M C^ t^
00 t^roc^ roOoO O t^OO OnOn^m loO O m O ^ rot^O «J~.
00 lOCSQC tO<N t^iOM Onm ooOoOO --^-rOM OnOO t^O m lO '^
V
loO r^oo O-
rO OOOOO OnOoO C^ lom t-«f^M m OO ^tO roOsrOioOsroO
OOO •^MOOO cs O t^voiN OOOO TtP< M O\00 \0 O u-i '^ T)- r^.
'**
O ro N 0\vO 'd- r^ •* C^ N M O VOVO 0\r>.t^N H Os-^t^-CS r^rf
M o r^Ti-c^ o r^uocon Os«>-ioroiH 0 Onoo r^ lo lo -^ ■^ co f^.
H«
O vO T)- 0) u-,
OOOOO O^OO rot^ON'^t^ror^N O^OnO r^OO On to On lO m OO
W M On I>~\0 ^<N 000^^^O'v^<N h OnOO COO lO^'^rOfOrOC^
M
t^ to M OnO
(N to 04 O OnOO m 0\nO tON IN Ooor^O '^ ■*vO On to M CO ^0)
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„MMMMMMMMMWO4O10404Ol
I
HORSE-POWER, BELTS AND SHAFTING
Horse-Power
. Horse-power is an arbitrary unit of measurement which has been
adopted for measuring the work of engines or machines. It is given
as 33,000 foot pounds per minute which means i pound Hfted 33,000
feet per minute or 33,000 pounds Hfted i foot per minute or 330
pounds lifted 100 feet per minute, or any combination which gives
33,000 foot pounds per minute.
Steam Engine Horse-Power
In a steam engine it means the effective steam pressure per square
inch, times the length of piston movement per revolution in feet,
times the piston area in square inches, times the number of revolu-
tions per minute, and all divided by 33,000. This is easily remem-
bered by the formula
PLAN
where
33000
P = mean effective pressure per square inch.
L = length of a double stroke in feet.
A = area of piston in square inches.
N = number of revolutions per minute.
Electrical Power
As compared with electrical units the mechanical horse-power
equals 746 watts or nearly f of a kilowatt. So that a kilowatt (1000
watts) equals 1.34 horse power.
Gas Engine Horse-Power
The A. L. A. M. rating for gasoline engines, which means the rat-
ing adopted by the American Licensed Automobile Manufacturers, is
based on the assumption that the piston speed is 1000 feet per minute
in all cases. This gives 1500 revolutions per minute for a 4-inch
stroke motor, which is about average practice. Since the defeat of
the Selden patent the A. L. A. M. has ceased to exist and this is now
known as the S. A. E. standard (Society of Automobile Engineers).
420
AUTOMOBILE MOTOR HORSE-POWER
421
S. A. E. (A. L. A. M.) HORSE-POWER RATING
D^ X N
The formula adopted is and based on 1000 feet per min-
2-5
ute piston speed. D is the cylinder bore, N the number of cylinders,
and 2.5 a constant, based on the average view of the Mechanical
Branch as to a fair conservative rating.
Table or Horse-Power for Usual Sizes of Motors, Based on
S. A. E. (A. L. A. M.) Formula
B02.E
Horse-Power
Ins.
M/M
I Cyl.
2 Cyls.
4 Cyls.
6 Cyls.
2|
64
2i
5
10
15
2I
68
2f
5^
II
I6i
2j
70
3,
6
I2tV
l8i
2I
73
3t6
6f
I3I
19I
3
76
^l
73-
I4I
2if
3i
79
3H
7-f
i5f
23T6
3j
83
4i
82
16/0
25I
3f
85
41^6
9l
i8i
27f
4
89
4t^o
9*
10^
i9f
^9^
31
92
4
20i
3if
4
95
5f
III
22i
33I
3I
99
6
12
24
36tV
4
102
6f
I2|-
13!
25f
38I
4l
105
6H
27i
40t^o
4i
108
7i
I4I
28A
43f
4f
III
7f
15 l¥
3of
45if
42
114
8to
i6i
32f
48I
4-
118
8x6
i7i
34i
5if
4t
121
9^
18
36tV
•54tV
4l
124
9I
19
38
57
5
127
10
20
40
60
5i
130
io|
21
42
63
si
^33
II
22
44x0
66i
5f
^37
11^
23
46
69tV
4
140
I2,V
I2f
'H
48f
72f
5f
143
25-^
50I
75-t
5f
146
'4,
262
53
792
5l
149
i3if
278
55i
82^
6
^52
i4i
28t
57l
86f
To simplify reading of the above, the horse-power figures are
approximate, but correct within vne-sixteenth.
422 HORSE-POWER, BELTS AND SHAFTING
DRIVING POWER OF LEATHER BELTS
The question of the proper size of a leather belt for a given power
transmission resolves itself into a question of selecting various fac-
tors. These factors have been worked out by experiments, by ana-
lytical methods, and in practice.
The horse-power that a belt will transmit depends upon the effective
tension and the belt speed. The effective tension depends upon
the difference in the tensions of the two sides of the belt and on
the surface friction, which depends upon the ratio of the tensions
and the angle of belt contact with pulley.
Experiments and practice have shown that a belt of single thick-
ness will stand a stress of 60 pounds per inch of width and give good
results, that is, it will only require an occasional taking up and will
have a fairly long life. The corresponding ^'alues for double and
triple belts are 105 and 150 pounds per inch of width provided the
pulleys are not too small.
Experiments have sho\\Ti that on small pulleys the ratio of the
tensions should not exceed 2, on medium pulleys 2.5, and on large
pulleys 3. The larger the pulley, the better the contact; also the
thinner the belt, the better the contact for the same size of pulley.
When the pulley diameter in feet is three times the thickness of the
belt in inches, or in this proportion, wx get equivalent results for
different thicknesses of belts. This gives us a method of classifying
our pulleys. The belt has to adjust itself in passing over a pulley
due to its own thickness. Some adjustment is also necessary on
account of the crowning of the pulley. These adjustments account
for the different ratios for the various pulley diameters. The effects
of the crown and pulley diameters are not usually considered in belt
rules, although they should be. The ratios given are for 180 degrees
wrap and decrease with less contact.
The creep of the belt depends upon its elasticity and the load,
and experiments have shown that this should not. exceed i percent,
in good practice. In order to keep this creep below i per cent, it
is necessary to limit the difference of tension per inch of width 6f
single belt to 40 pounds. The corresponding values for double and
triple belts are 70 and 100 pounds per inch of width. These figures
are based on an average value of 20,000 for the running modulus of
elasticity of leather belting.
Table i has been prepared" on the basis of these limitations and
gives a value for the factor or constant F in the equation
H.P. = y^orW=^i^
in which F P is the horse_-power, V the belt velocity in feet per minute,
and W the width in inches.
Table 2 gives corrected values for F, when the arc of contact or
wrap is greater or less than 180 degrees. On large pulleys the
creep may exceed i per cent, if the wrap is over 180 degrees, as
the increased friction gives a greater difference of tensions.
To illustrate the use of the tables, we will take the followmg
examples:
FACTORS FOR BELT POWER
423
O ^
00
o o
OS q
O O d ro O
fO O 10
c^ O
o d «N o
O »o O <N O
O O O ro 10
r- f^ O
On O
00 10
o vo d <N o
ON
a (U « .r^
C O
.2-i
2 S3 .„ ..
0
8^8
rj" cs M
0 0 ro
00 r^MD
10 -^ Tt
CO
000
fO !>- rO
ro M 0
HUM
000
10 ^ Tj-
0
M
t^ 0 00
<N M ON
000
CO POO
CN) 10 0
10 ';^ -si-
10
<N 0 On
M M
0 0 fO
LO Tf ro
M
M c^oo
M
000
0 10 10
c§2n§
^ ^ ro
R
w a^oo
000
LO ^ O^
0 10 Tt
000
VO On "*
Tt fo fO
°i
000
0 (N CT)
H QnOO
nO 10 '^
000
■Ti- t^ ro
^ CO ro
\
O'oo 00
000
M 0 »o
NO lO Tl-
000
Tt CO ro
\
^5R
0 00 t^
8n^^
2 ^2
^ ro CO
000
0 00 t^
t^ t-- ro
10 ^ rt-
8^8
Tt CO CO
CM
CM
000
N^Ngg
*0 't 't
gNsa
fO CO <N
424 HORSE-POWER, BELTS AND SHAFTING
How much horse-power will a 4-inch single belt transmit at a speed
of 4600 feet per minute passing over a 12-inch pulley? The factor
is 920, therefore,
46^X4 = 20 H.P.
920
How wide should a belt be in order to transmit 50 horse-power
at 2000 feet per minute on a 36-inch pulley?
W= ^° X ^^° = 20.7-inch single belt.
2000
This gives a \\adth of single belt beyond the usual limit, 8 inches
being considered good practice for the maximum width of a single belt.
W =-5£_>li^ ^ i^-inch double belt.
2000
How wide should a single belt be in order to transmit 2 horse-
power at 600 feet per minute over a 4-in. puUey ^vith 140 deg. wrap?
In this case we take the factor iioo from Table i and in Table 2
find a corrected value for iioo under 140 degrees of 1270.
W = — - — — = 4.2 $-inch single belt.
000
How wide a belt is required for 300 horse-power at 2000 feet per
minute over a io-fo6t pulley?
W = — = 70.5-inch double belt.
2000
This is too wide. Good practice calls for a change to triple at
48 inches unless for some special reason a narrower belt is necessary.
lY = ^°° X ^^° = 4g.s-inch triple belt.
2000
The results given by these factors are well within working values
and the belts wiU probably transmit 50 per cent, more power than
these factors, but at the expense of the life of the belt. A liberal
allowance at the beginning means less annoyance, fewer delays in
taking up the belts, longer life and less cost for renewals and repairs.
Belt speeds of 4000 to 4800 ft. should rarely be exceeded.
Transmission of power in miU work is by gearing, by shafting,
by electric motors, and by leather and rope belting, and which of
these should be used in a particular case is a problem for the engineer
in charge to determine.
For successful v/ork the pulleys must be large in diameter and
must have a smooth surface where the rope bears upon them. The
speed and the load on the rope must also be such as experience has
shown to be economical. When these conditions are fulfilled, a
rope drive is a very satisfactory method of transmitting power.
The table shows the horse-power of driving ropes and the diameter
of pulleys that should be used for this purpose. This table takes
into consideration the effects of the centrifugal force, so that the
strain on the rope is constant on the driving side in transmitting the
tabular power, no matter what the speed may be. While many
engineers recommend a much larger horse-power, we beheve the
estimates here given are advisable except in temporary installations.
DATA OF MANILA ROPE
Horse-Power oe Manila Rope
425
Dia.
of
Rope
Velocity, Feet per Minute
I, COO
1,500
2,000
2,500
3,000
3,500
4,000
4,500
5, 000
5,500
6,000
3
4
2.3
3-3
4-3
5-2
6.0
6.6
7.2
7-3
7.4
7.3
6.9
i
3-0
4-5
5-9
7.0
8.2
9.0
9.6
9.8
lO.O
9.6
9.0
4.0
5-9
7-7
9.2
10.6
11.8
12.7
12.9
13.0
12.7
12.0
'!
5-0
7.5
9-7
II.6
13-5
14.9
16.0
16.3
16.7
16.5
15-3
t1
^•3
9.1
12.0
14-3
ib.7
18.5
20.0
20.2
20.7
20.1
18.9
li
7-5
10.8
14.4
17.4
20.0
22.1
23-7
24-5
24.6
24.0
22.3
1^
9.0
13-5
17.4
20.7
23.0
26.3
28.7
29.0
29.5
28.6
26.7
if
10.5
15-5
20.1
24-3
27.9
30.8
32.9
34-1
34.3
33-3
31.0
if
12.3
18.0
23.6
28.2
32.7
36.4
38.5
39-4
40.5
3«.7
36.0
2
16.0
23.2
30.6
46.8
42.5
46.7
50.0
51-7
52.8
50.6
47-3
2i
20.0
29.6
38.6
46.6
53.6
59.2
63.6
6=;.8
66.3
64.4
60.3
2^
25.0
36.6
47-7
57-5
66.0
71.2
78.0
80.0
81.0
79.0
73-8
Data of Manila Transmission Rope
^
S
Length of SpUce,
1
e
.2
Q
"o
•5
a
en
i
<
Feet
•sj
il
J,1
h
"0
1
2
1
So.S
.2
Q
3
1
<
r
CO
w
't
gCAl
rt 0 a
1
•5625
.20
3,950
112
6
8
28
760
i
.7656
.26
5,400
153
6
«
32
650
I.
•34
7,000
200
7
10
14
36
570
li
1.2656
.43
8,900
253
7
10
16
40
510
U
1.5625
•53
10,900
312
7
10
16
46
460
1.8906
•65
13,200
378
8
12
16
50
415
2.25
•77
15,700
450
8
12
18
54
380
if
2.6406
.90
18,500
528
8
12
18
6o-
344
^4
3.0625
1.04
21,400
612
8
12
18
64
330
2
4-
1.36
28,000
800
9
14
20
72
290
24
5-0625
1-73
35,400
1,012
9
14
20
82
255
2^
6.25
2.13
43,700
1,250
10
16
22
90
230
Weight of transmission rope = .34 X diameter.^
Breaking strength = 7,000 X diameter.^
Maximum allowable tension . = 200 X diameter.^
Diameter smallest practicable sheave. . = 36 X diameter.
Velocity of rope (assumed) = 5,400 feet per minute.
426 HORSE-POWER, BELTS AND SHAFTING
BELT FASTENINGS
The best fastening for a belt is the cement splice. It is far
beyond any form of lacing, belt hooks, riveting, or any other
method of joining together the ends of a belt. The cement joint is
easily applied to leather and to rubber belts, but to make a good
cement splice in a canvas belt requires more time and apparatus
than is usually at hand. Good glue makes a fine cement for leather
belts, and fish glue is less affected "by moisture than the other.
Many of the liquid glues are. fish glue treated with acid so as not
to gelatinize when cold. A little bichromate of potash added to
ordinary hot glue just before it is used will render it insoluble in
water. Both lap and wedge joints are used.
Belt Hooks
There are many styles of belt hooks in use, some of the more com-
mon kind being shown in Figs, i, 2, 3 and 4. Fig. 2 is practically
a double rivet, Fig. 3 a malleable iron fastening, although similar
hooks have been made of pressed steel, and Fig. 4 is the Blake stud,
which has the advantage of not weakening the belt but makes a
hump on the outside where the ends turn up. Fig. 5 is the Bristol
hook of stamped steel which is driven in the points turned over on
the other side. Fig. 6 is the Jackson belt lacing and is applied
by a hand macliine which screws a spiral wire across the ends of a
belt. These are then flattened and a rawhide pin or a heavy soft
cord used as a hinge joint between them. These joints are probably
equal to 90 per cent, of the belt strength.
Lacing Belts
Belts fastened by lacing are weakened according to the amount
of material punched out in making the holes to receive the lacing.
It is preferable to lace with a small lacing put many times, through
small holes. Such a joint is stronger than a few pieces of wide lacing
through a number of large holes. Figs. 7 and 9 illustrate two forms
of belt lacing, the latter being far preferable to the other. The lacing
shown by Fig. 7 is in a double leather belt 5 inches wide. The width
makes no difference as the strength is figured in percentage of the
total width. There are four holes in this piece of belt, each hole
f inch in diameter. The aggregate width thus cut out of the belt is
4Xf inch=-^/ = i^- inches. Then 1.5 -=-5 =0.30, or 30 per
cent, of the belt has been cut away — ^nearly one-third of the total
strength.
Another Method of Lacjng
In Fig. 9 a different method is followed. Instead of there being a
few large holes, there are more smaller ones — one fourth more, in
fact. There are five holes, each j\ inch in diameter, making a
total of If inch or 0.9375 -r S = i8f per cent., leaving SiJ per
cent, of the total belt strength against 70 per cent, in the belt with
large holes. A first-class double leather belt will tear in two under
BELT HOOKS AND LACINGS
427
a strain of about 500 pounds to each lace hole, the strain being
applied in the holes by means of lacings.
The belt shown by Fig. 9 has 81-4- per cent, of 1.875 square inches
of section, = 1.525 square inches left after cutting out the five holes.
This amount is good for 3000 X 1.875 = 5625 pounds breaking
strain, and as the lacing will tear out under 2500 pounds, it will be
seen that we cannot afford to use lacings if the full power of the
leather is to be utilized. This, under a factor of safety of 5, would
be 1 1 25 pounds to the square inch, or 11 25 X 1-525 = 1715 pounds
e:=^
FIG. I
PI.Gv 8 FIG. 9
Belt Hooks and Lacings
working strain for the belt, ori7i5-7-5=343.5 pounds to each
lace. This, too, is too much, as it is less than a factor of safety of 2.
The belt to carry 40 pounds working tension to the inch of width
must also carry about 40 pounds standing tension, making a strain
of 80 pounds to the inch, or 80 X 5 = 400 pounds. This is a better
showing, and gives a factor of safety of 2500 -r- 400 = 6J. Still, we
are wasting a belt of 5625 pounds ultimate strength in order to get
from it 400 pounds working strain. This means a factor of safety
of over 14 in the body of the belt but of only 6^ at the lacing, which
shows the advantage of a cement splice.
Fig. 10 shows a method sometimes used t© relieve the lace-holes
of some of the strain. Double rows of holes are punched as at o &,
and the lacing distributed among them. As far as helping the
428
HORSE-POWER, BELTS AND SHAFTING
strength of the belt is concerned, this does nothing, for all the stress
put upon the belt by the lacing at c must be carried by the belt sec-
tion at a; therefore this way of punching holes does not increase the
section strength. Neither does staggering the holes as shown at d
and e. The form of hole-punching shown at a & c is desirable for
another reason. It distributes the lacing very nicely and does not
make such a lump to thump when it passes over the pulleys.
ALINING SHAFTING BY A STEEL WIRE
A STEEL wire is often used for ahning shafting by stretching it
parallel with the direction of the shaft and measuring from the shaft
to the wire in a horizontal direction. This steel wire can also be
used for leveling or alining in a direction at right angles to the other,
Sags of a Steel Alining Wire for Shafting
Distance in Feet, from Reel to Point of Measurement
3°
40
50
60
70
90
130
140
270
*.
260
SL
2=;o
^
^
240
230
220
.9
210
^
200
2
190
-s
tSo
Pi
170
s
160
ii
150
"S
140
k
130
fl
120
no
100
"C
90
(-)
80
70
60
so
40
30
If
itV
t13
I32
iM
T 9
I 3" 2
III
iH
I32
itV
■••3 2
it\
13^
'ft
53
64
If
f
if
ill
iH
IT6
itV
'ft
13
tb;
45
fi4
t13
lii
1*1-
lT6
ItV
i\
5 3
23
it
ifl
Its
■■■3 2
I ¥'2
'If
6¥
II
II
If
I
I
6^
Sag of the Wire in Inches
SAGS OF A STEEL ALINING WIRE
429
by making vertical measurements, if it is stretched imder established
conditions and if the sags at the points of measurement are known.
The accompanying table gives the sags in inches from a truly level
line passing through the points of support of the wire, at successive
points beginning 10 feet from the reel and spaced 10 feet apart for
a No. 17 Birmingham gage high grade piano wire, stretched with a
weight of 60 pounds, wound on a reel of a minimum diameter of
three and one-half inches and for total distances between the reel
and point of support of the wire varying by increments of 10 feet
from 40 to 280 feet. Thus a wire of any convenient length, of the
kind indicated, can be selected, so long as this length is a multiple
of ID feet and between the limits specified, and the table gives the
sags from a truly level line at points 10 feet apart for its entire length
when it is stretched under the conditions designated. These sags
Sags of a Steel Alining Wire for Shafting
Distance in Feet, from Reel to Point of Measurement
280
270
260
250
240
230
220
210
200
190
180
170
160
ISO
Iff
l6¥
I32
t13
I32
lif
u
H
If
13
"32
64
[6c
^64
III
I32
l6\
u
190
T 1 O
132
lii
ItV
T-a-i
l64
iH
1/4
15
230 240
ItV
250
260
if
270
Sag of the "Wire in Inches
being known, direct measurements can be made to level or aline
a shaft by vertical measurements.
The method was originally developed for alining the propeller
shafts of vessels, but it is equally serviceable for semi -flexible shafting,
as factory line shafts.
Speed of Shafting
Line shaft speed varies with machinery it drives. Probably 250
r.p.m. is an average today, with cases of 400 r. p. m. even on 4-in. shafts
and 600 to 700 r. p. m. on 2-in. shafts for high speed machinery.
430
HORSE-POWER, BELTS AND SHAFTING
HORSE POWER OF STEEL SHAFTING
For Line Shapt Service
^
Revolutions per
Minute
^.^
^ 'S>
III
lOO
125
150
17s
200
225
250
300
350
400
It\
2.4
3-1
3-7
4-3
4.9
5-5
6.1
7-3
8-5
9-7
It'b
4-3
5-3
6.4
7-4
«-5
9-5
10.5
12.7
14.8
16.9
6.8"
H
0.7
8.4
lO.I
II. 7
13-4
15-I
16.7
20.1
23-4
26.8
7-2"
i\%
lO.O
12.5
15-0
17.5
20.0
22.5
25-0
30.0
35-0
40.0
8.2"
2 fa
14-,^
17.8
21.4
24.9
28.5
32.1
35-6
42.7
49-8
57.0
8.9"
2th
iq.5
24.4
29-3
ZA.X
39-0
44-1
48.7
5«-5
68.2
78.0
9.6"
2U
26.0
32.5
39-0
43-5
52.0
5«-S
65.0
78.0
87-0
104.0
10.2"
2iii
,S,V8
42.2
50.6
S9-I
67-5
75-9
84.4
101.3
118.2
135.0
10.8"
3t'«
4.^-o
,S3.6
64.4
7S-I
85.8
96.6
107.3
128.7
150.3
171. 6
1 1. 4*
M'-.
S.Vb
67.0
79-4
93-8
107.2
120. 1
•T34-0
158.8
187-6
214.4
12.0"
■>\k
65-9
82.4
97-9
iiS-4
121.8
148.3
16^.8
195-7
230.7
243.6
12.5"
Mi
80.0
lOO.O
120.0
140.0
160.0
iSo.o
200.0
240.0
280.0
320.0
4T'n
113-9
142.4
170.8
199-3
227.8
256.2
284.7
341-7
398.6
. 455.6
4ls
I,S6.,S
195-3
•234-4
273-4
312-5
351-5
390.6
468.7
546.8
625.0
5l
207.9
260.0
311-9
363-9
415-9
459-9
520.0
623.9
727.9
830.0
0
270.0
337-5
405-0
472-5
540.0
607.5
675-0
810.0
945-0
1080.0
bi
,U3.3
429.0
514-9
600.7
6S6.5
772.4
858.0
1029. 0
1201.0
1372.0
7
428.8
535-9
643-1
750.3
847-5
964-7
1071-9
1286.0
1500.0
1695-0
8
640.0
Soo.o
960.0
1126.0
12S0.0
1440.0
1600.9
1920.0
2240.0
2560.0
This table is based on the formula
M
80
For heavier work use M
D^XR
For head and jack shafts, supported by bearings close to main
sheave or pulley so as to prevent transverse strain, the following
formula may be used with safety:
D'XR
M =
125
D = Diameter of shaft in inches.
R = Number of revolutions per minute.
M = Horse-power.
Deflection of shafting from weight of pulleys and draw of belting
should not be allowed in excess of .001 per foot, as this action adds
very rapidly to the power cost. If this deflection is at a clutch,-
sleeve or roller bearing, any of them may be ruined easily and quickly.
It can be reduced by using more hangers.
SPEEDS OF PULLEYS AND GEARS
The fact that the circumference of a pulley or gear is alwaj^s
3.1416 or 37- times the diameter makes it easy to figure speeds by
considering only the diameter of both driver and driven pulleys.
Belting from one 6-inch pulley to another gives the same speed to
both; but if the driving pulley is 16 inches and the driven pulley
only four inches it is clear that the small pulley will turn 4 times for
SPEEDS OF PULLEYS AND GEAHS
431
every turn of the large pulley. If this is reversed and the small
pulley is the driver, the large pulley will only make one turn for
every four of the small pulley. The same rule applies to gears if
the pitch diameter and not the outside diameter is taken. The fol-
lowing rules have been arranged for convenience in finding any
desired information about pulley or gear speeds.
Diameter of Driving Pulley
Diameter of Driven Pulley
Speed of Driving Pulley
Diameter of Driving Pulley
Speed of Driving PuUey
Speed of Driven Pulley
Diameter of Driving Pulley
Diameter of Driven Pulley
Speed of Driven Pulley
Diameter of Driven Pulley
Speed of Driven Pulley
Speed of Driving Pulley
Speed of Driven Pulley
Diameter of Driven Pulley
Speed of Driving Pulley
Diameter of Driving Pulley
Multiply Diameter of
Driving Pulley by its
Speed and divide by
Diameter of Driven
Pulley.
Multiply Diameter of
Driving Pulley by its
Speed and Divide
by Speed of Driven
Pulley.
Multiply Diameter of
Driven Pulley by its
Speed and Divide by
Diameter of Driving
Pulley.
Multiply Diameter of
Driven Pulley by its
Speed and Divide
by Speed of Driving
Pulley.
These rules apply equally well to a number of pulley belts to-
gether or to a train of gears if all the driving and all the driven pulley
diameters and speeds are grouped together.
TABLES OF CIRCUMFERENTIAL SPEEDS
The tables on pages 432-435 which give circumferential speeds,
can be used for obtaining gear and belt speeds and the speed of
revolving parts of high-speed motors.
For diameters greater than those given in the tables, the speeds
can be obtained by adding together the speeds for two diameters
whose sum equals that of the diameter for which we require the
speed. For example, to find the speed at a 120-inch diameter and
200 revolutions per minute, the following calculation is readily made :
Speed for 100-inch diameter — 5236 feet.
Speed for 20-inch diameter — 1047 feet.
Speed for 120-inch diameter — 6283 feet.
To interpolate, we can use the values given for speed for i- to
lo-inch diameters, dividing them by 10, 100, 1000, etc., to obtain
speeds for tenths, hundredths, thousandths, etc. For instance, if
the speed for 550 revolutions per minute and 46.186-inch diameter
is required, we proceed as follows:
For 46 in. diameter speed = 6623 ft.
For 0.1 in. diameter = -^ of i-in. diameter speed = 14.4 ft.
For 0.08 in. diameter = i^^ of 8-in. diameter speed = 11. 5 ft.
For o.oo6 in. diameter = i^Vo of 6-in. diameter speed = . o.g ft.
For 46.186 in. diameter speed = 6650 ft.
432
HORSE-POWER, BELTS AND SHAFTING
Circumferential Speeds in Feet per Minute
{See page 431)
Revolutions per Minute
50
100
150
200
250
300
350
400
450
500
S50
I
13
26
39
52
65
79
92
los
118
131
144
2
26
52
79
105
131
157
183
209
236
262
288
3
39
79
118
157
196
236
275
3^4
353
393
432
4
52
los
157
209
262
314
367
419
471
523
576
5
65
131
196
262
328
393
458
524
589
654
720
6
79
157
236
314
393
471
550
628
707
785
863
7
92
183
275
367
458
55?
641
IH
82s
916
1,008
8
105
209
314
419
524
628
733
838
942
1,047
1,152
9
118
236
353
471
589
707
82s
942
1,060
1,178
1,296
10
131
262
393
524
655
785
916
1,047
1,178
1,309
1,440
II
144
288
432
576
720
864
1008
1,152
1,296
1,440
1,584
12
157
314
471
628
785
943
IIOO
1,257
1,414
1,571
1,728
13
170
340
511
681
851
1021
1191
1,361
1,532
1,701
1,872
14
183
367
550
733
916
IIOO
1283
1,466
1,649
1,832
2,016
IS
196
393
589
785
982
1178
1375
1,571
1,767
1,963
2,160
16
209
419
628
838
1047
1257
1466
1,675
1, 88s
2,094
2,304
17
223
445
668
890
1113
1335
1558
1,780
2,003
2,22s
2,442
18
236
471
707
943
1178
1414
1649
1,885
2,121
2,356
2,592
19
249
497
746
995
1244
1492
1741
1,990
2,238
2,487
2;736
20
262
524
785
1047
1309
1571
1833
2,094
2,356
2,618
2,880
1
21
275
550
825
HOC
1374
1649
1924
2,199
2,4 74
2,749
3,024
22
288
576
864
II52
1440
1728
2016
2,304
2,592
2,880
3,168
1
23
301
602
903
1204
1505
1806
2107
2,409
2,710
3,011
3,312
24
314
628
943
1257
1571
1885
2199
2,513
2,827
3,142
3,456
^c
25
327
655
982
1309
1636
1963
2291
2,618
2,945
3,273
3.600
S
26
340
681
1021
I36I
1702
2042
2382
2,723
3,063
3,403
Hii
^
V
27
353
707
1060
I4I4
1767
2121
2474
2,827
3,181
Hl"^
3,888
E
28
367
733
IIOO
1466
1837
2199
2566
2,932
3,299
3,665
4,032
.2
29
380
759
II39
I5I8
1898
2278
2657
3,037
3,417
3,796
4,176
s
30
393
785
II78
I57I
1964
2356
2749
3,142
^ 534
S,02 7
4,320
31
406
812
I2I7
1623
2029
2435
2840
3,246
3,652
4,058
4,464
32
419
838
1257
1676
2094
2513
2932
3,351
3,770
4,189
4,608
33
432
864
1296
1728
2160
2592
3024
3,456
3,888
4,320
4,752
34
445
890
1335
1780
2225
2670
3115
3,560
4,006
4,451
4,896
35
458
916
1375
1833
2291
2749
3206
3,66s
4,123
4,581
5,040
36
471
943
I4I4
1885
2356
2827
■3299
3,770
4,241
4,712
5,184
37
484
969
1453
1937
2422
2906
3390
3,875
4,359
4,843
5,328
38
497
995
1492
1990
2487
2985
3482
3,979
4,477
4,974
5,472
39
511
1021
1532
2042
2553
3063
3573
4,084
4,595
5,105
S,6i6
40
524
1047
I57I
2094
2618
3142
3665
4,189
4,712
5,236
5,760
41
537
1073
I6I0
2147
2683
3220
3757
4,294
4,831
5,367
5,904
42
550
1 100
1649
2199
2749
3299
3848
4,398
4,948
5,498
6,048
43
563
1126
1689
2251
2S14
3377
3940
4,503
5,066
5,629
6,192
44
576
1152
1728
2304
2880
3456
4032
4,608
5,184
5,760
6,336
45
589
1178
1767
2356
2945
3534
4123
4,712
5,301
5,891
6,480
46
602
1204
1806
2408
3011
3613
4215
4,817
5,419
6,021
^^3§
47
615
1231
1846
2461
3076
3692
4307
4,922
5,537
6,152
6,768
48
628
1257
1885
2513
3142
3770
4398
5,027
5,655
6,283
6,912
49
641
1283
1924
2566
3207
3849
4490
5,131
5,773
6,414
7,056
50
65s
1309
1963
2618
3273
3927
4581
5,236
5,891
6,545
7,200
TABLES OF CIRCUMFERENTIAL SPEEDS
433
CmCUMTERENTIAL SPEEDS IN FeET PER MiNUTE
(See page 431)
Revolutions per
Minute
50
100
150
200
250
300
350
400
450
500
550
51
668
1335
2003
2670
3338
4006
4673
5,341
6,008
6.676
7,343
52
681
1361
2042
2723
3403
4084
4764
5,445
6,126
6,807
7,487
53
694
1388
2o8t
2775
3469
4163
4856
5,550
6,244
6,938
7,631
54
707
1414
2I2I
2827
3534
4241
4948
5,655
6,362
7,069
7,775
55
720
1440
2160
2880
3600
4320
5040
5,760
6,480
7,199
7,919
56
733
1466
2199
2932
3665
4398
5131
5,864
6,597
7,330
8,063
57
746
T492
2238
2985
3731
■4477
5223
5,969
6,715
7,461
8,207
58
759
1518
2278
3037
3796
4555
5314
6,074
6,833
7,592
8,351
59
772
1545
2317
3089
3862
4634
5406
6,178
6,951
7,723
8,495
60
785
1571
2356
3142
3927
4712
5498
6,283
7,069
7,854
8,639
61
799
1597
2395
3194
3992
4791
5589
6,388
7,186
7,985
8,783
62
812
1623
2435
3246
4058
4870
5681
6,493
7,304
8,116
8,927
63
825
1649
2474
3299
4123
494»
5773
6,597
7,422
8,247
9,071
64
838
1676
2513
3351
4189
5027
5864
6,702
7,540
8,378
9,215
05
851
1702
2552
3403
4254
5105
5956
6,807
7,658
8,508
9,359
66
864
1728
2592
3456
4320
5184
6048
6,912
7,775
8,640
9,503
67
877
1754
2631
3508
4385
5262
6139
7,016
7,893
8,770
9,647
68
890
1780
2670
3560
4451
5341
6231
7,121
8,011
8,901
9,791
69
903
1806
2710
3613
4516
5419
6322
7,226
8,129
9,032
9,935
,0
.916
1833
2749
366s
4581
5498
6414
7,330
8,247
9,163
10,079
71
929
I8S9
2788
3718
4647
5576
6506
7,435
8,365
9,29!
10,223
'Q
72
943
1885
2827
3770
4712
5655
6597
7,540
8,482
9,425
10,367
-s
73
956
1911
2867
3822
4778
5733
6689
7,644
8,600
9,556
10,511
c
74
969
1937
2906
3875
4843
5812
6781
7,749
8,718
9,687
10,655
10,796
C3
75
982
1964
2945
3927
4909
5890
6872
7,854
8,836
9,818
76
995
1990
2985
3979
4974
5969
6964
7,959
8,954
9,948
10,943
1
77
1008
2016
3024
4032
5040
6048
7056
8,063
9,072
10,079
11,087
78
1021
2042
3063
4084
5105
6126
7147
8,168
9,189
10,210
11,231
79
1034
2068
3102
4136
5171
620s
7239
8,273
9,307
10,341
11,375
P
80
1047
2094
3142
4189
5236
6283
7330
8,378
9,425
10,472
11,519
81
1060
2121
3181
4241
5301
6362
7422
8,482
9,543
10,603
11,663
82
1073
2147
3220
4294
5367
6440
7514
8,587
9,660
10,734
11,807
83
1087
2173
3259
4346
5432
6519
7605
8,692
9,778
10,865
11,951
84
1 100
2199
3299
4398
5498
6597
7697
8,797
9,896
10,996
12,099
85
1113
2225
3338
4451
5563
6676
7789
8,901
10,014
11,127
12,235
86
1126
2251
3377
4503
5629
6754
7880
9,006
10,132
^^'^Vo
12,383
87
1139
2278
3417
4555
5694
6833
7972
9,111
10,249
11,388
12,527
88
1152
2304
3456
4607
5760
6912
8063
9,215
10,367
11,519
89
1161
2330
3495
4660
5825
6990
8155
9,320
10,485
11,650
90
1178
2356
3534
4712
5891
7069
8247
9,425
10,603
11,780
91
1191
2382
3574
4765
5956
7147
8338
9,530
10,721
11,912
92
1204
2408
3613
4817
6021
7226
8430
9,634
10,839
12,043
93
1217
2435
3652
4870
6087
7304
8522
9,739
10,956
12,174
94
1231
2461
3692
4922
6152
7383
8613
9,844
11,074
12,305
95
1244
2487
3731
4974
6217
7461
8704
9,948
11,192
12,436
96
1257
2513
3770
5027
6283
7540
8796
10,053
11,310
12,566
97
1270
2539
3809
5079
6349
7618
8888
10,158
11,428
98
1283
2566
3849
5131
6414
7697
8980
10,263
11,545
99
1296
2592
3888
5183
6480
7775
9071
10,367
11,663
100
1309
2618
3927
5236
6545
7854
9163
10,472
11,781
434
HORSE-POWER, BELTS AND SHAFTING
00 t^^ lO ■N^ M M O OiOO vO vo ^ ro cs O OvOO t^^O ■* rO M
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J^ ■* w 00 »0 CM OvO coo t~--+HOO »OtN (^O CO O t- •* M
M CO lOO 00 O iH CO »o r^GO O <M CO *o r^oo O m tj- lo t-; 0»
(H^H'i-rM'i-ri-rcrci'crcM'tNorcocococococo
r^rJ-H00iON0«^'ti-<00»OCM OvO co O t^ lo m OiO cO
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M co-^Ot^Oi-i CM Ttio t^oO O M CO ioO^00_ O; w tM ^O
MHHMMMtN'tNPrCMtN^erCM COCOCOCO
M CM CO -+ lOO t^OO 0\ O W CM CO ■* VOO t^<» 0> O w " CO
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rt|t<
Clr
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rt"-^ loloO O
rtIN wlc. H« HIN
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M M
r^
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BW
M W M W
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COCOtOCO'^tJ-^'t'O'"""^
saqouj ui aajauiBjQ
TABLES OF CIRCUMFERENTIAL SPEEDS
435
t- t^oo oooooo O' S S o 6 o o
lO'O O ^O O t^ t^ t^ r~00 OOOOOO OvOvO\0^0 O O O
L
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in t-00 O o<, "2 "2^„°9>
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' io\0 O O "O t^ f^
la^auiBiQ
fo^o o M -"tvo oi I
M ro^o 00 H rO<3C_ . _ _ . _ _ . _ _
rj-y3 00 O CO vo t^OO oi -"to 00 w ro lO f^ O cs tJ-vO Ov >
ro *-r> r^ O 01 -^vO 0» ►-f ro lo t^ O M -^O 0> tH v^ in t^ O csi 't^ O*
vo m vo\o"\o o o vo t^ t^ !>• t^co oooooooddio\ovdvo o o"o"o
<N M O O O OvoOOO
M (S ro ^ ■* too t-^
0*M roiOf^O^M ro
r^vo lo to rh .
CO O O M M rfj ^ u^^o t^oo Ov
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436
HORSE-POWER, BELTS AND SHAFTING
POWER REQUIRED BY MACHINE TOOLS
Swing
Inches
12
14
16
18
20-22
24-27
30
32-36
38-42
48-54
60-84
Engine Lathes
Horse-power
Average Heavy
work
1
2
I- I
1-2
2-3
3
5
5 - n
7^-10
10 -15
15 -20
20 -25
work
2
2-3
2-3
3-5
75-10
7§-IO
n-T-o
10 -15
15 -20
20 -25
25 -30
Axle Lathes
H.P.
Single 5- 7i-io
Double 10-15 -20
Locomotive axle .... 25
Wheel Lathes
Tailstock
Motor
H.P. H.P.
48-in. car wheel. . . 15-20 5
5 1-60 driv. wheel . . 15-20 5
79-84 25-30 5
90 30-40 S-lh
100 40-50 5-7I
Quartering attach-
ment 3-5
Cylinder Lathes
H.P.
40 in 15
40-in. heavy ...... 20
48 in 15
Vertical Boring Mills
Size Average Heavy
HP. H.P.
36-42 in. 5-^7^ 7^-10
50 in. 71 7i-io
60-84 in. 7I-10 10 -15
7-12 ft. 10 -15 30 -40
14-25 ft. 15 -25 30 -40
Horizontal Boring, Drilling
and Milling Machine
Dia.
Spindle
Horse-power
for Single Spindle
2,h-Ah
4I-5I
7^-10
5^6^ 10 -15
For double spindle, use double
the horse-power.
Cylinder Boring Mach.
Dia. Max. Boring Horse-
Spindle Diameter power
4 20 ^\
6 50 10
8 40 15
Miscellaneous
Loco, rod boring mach. 7i-io
Car-box boring mach.
6x12 and 5I X 10'' boxes 5-7^
Car- wheel borer 10-15
Planers
Size
24 X 24 in.
30 X 30 in.
36 X 36 in.
48 X 48 in.
60X 60 in.
72 X 72 in.
84 X 84 in.
100 X 100 in.
Horse-power
3- 5
5-7i
10-15
15-20
20-25
20-30
30
40
Note. — Normal length of bed
in feet is about \ the width in
inches.
Frog and Switch Planers
36X 12 in. 30
48 X 36 in. 30
Plate Planers
Niles Nos. 2 and 3 10
Niles No. 5 IS
Niles Nos. 6 and 7 20
Niles No. 8 20-25
POWER REQUIRED BY MACHINE TOOLS 437
Rotary Planers
Dia. Cutter Horse-power
24- 30 in. 5- 7 1
36- 42 in. 10
48- 54 in. 15
60- 72 in. 20-25
84-100 in. 30-40
Shapers
H.P.
i2-i6-in. stroke 2
i8-in. stroke 2-3
20-24-in. stroke 3-5
30-in. stroke 5 - 72
20-in. Traverse-head . . 7^
24-in. Traverse-head . . 10
Crank Blotters
Stroke Horse-power
^8 3-5
10-12 5
14 5 - 7I
16-18 7i-io
20-30 10 -15
Plain Millers
Table Feed Cross Feed H.P.
34 10 7I
42 12 10
SO 12 15
Universal Millers
Nos. i-i| 1-2
No. 2 3-5
No. 3 5 - 7I
No. 4 72-10
No. 5 10-15
Vertical Millers
Height Under Work
12-14 in. 5- 7i
18 in. 10
20 in. 15
24 in. 20
Vertical Slab Millers
24-in. width of work 7I
32-36-in. width of work ... 10
42-\n. width of work 15
Horizontal Slab Millers
Width Between
Horse-power
Housings
Average Heavy
24-30 in.
7^-10 10-15
36 in.
10 -15 20-25
60-72 in.
25 75
Cylindrical Grinders
Horse-power
Dia. Wheel
Average Heavy
10 m.
5 1\
14 in.
10 15
18 in.
10 15
Emery Grinders
No. Wheels
Dia. H.P.
2
6 in. \- I
2 .
10 m. 2
2
12 m. 3
2
18 in. S - l\
2 24-
-26 in. 7i-io
Misc. Grinders
Type Horse-power
Wet tool 2-3
Flexible swing 3
Angle cock 3
Piston rod 3
Twist driU 2
Automatic tool 3-5
Car wheel 30
Buffing Heads
No. Wheels
Dia.
H.P.
2
6
\-\
2
10
I -2
2
14
3 -5
Vertical Drills
Size H.P.
12-20 in I
24-28 in 2
30-32 in 3
3^40 in 5
5c^o in 5 -yi
Sensitive drills up to ^-in. ^ |
43S
HORSE-POWER, BELTS AND SHAFTING
Radial Drills
Horse-power
Size Average Heavy
3-ft. arm ' 1-2 3
4-ft. arm 2-3 5 " 7l
5-6-7ft. arm 3-5 5 - 7i
8-9-10 ft. arm 5-72 72-10
Multi.-Spindle Drills
Size of Drills Up to H.P.
sV- 4 6-10 spindle 3
Tt- f 6-10 spindle 5
TE~ h 6-10 spindle 7^
J- i 6-10 spindle 10
|- I 6-10 spindle 10-15
2 4 spindle 7^
Gear Cutters
Size Horse-power
36 X 9 in. 2-3
48 X 10 in. 3-5
30-60 X 12 in. 5-75
72 X 14 in. 7^-10
64 X 20 in. 10-15
Cold Saws
Dia. Saw Horse-power
20 in. 3
26 in. 5
32 in. 71
36 in. 10-15
42 in. 20
48 in. 25
Hacksaws |
Bolt Cutters
Single Horse-power
I, li, I^ in 1-2
if , 2 in 2-3
2I, 3I in 3-5
4, 6 in. 5-7I
1, i| in. double 2-3
2, 2I in. double 3-5
I, i|, 2 in. triple 3-7^
Bolt Pointers
i|, 2I in 1-2
Nut Tappers
I, 2 in. 4-spindle 3
2 in. 6-spindle 3-5
2 in. lo-spindle 5
2 in. nut facer 3
Pepe Threading and Cutting
OFF Machines
Size of Pipe Horse-power
J- 2 ill. 2
I- 3 in. 3
li- 6 m. 3-5
2 - 8 in. 3-5
3 -10 in. 5
4 -12 in. 5
8 -l8 in. 7I
24 in. 10
Hammers
Size Horse-power
15- 75 lb. 1-5
100-200 lb. 5 -75
Drop hammers require approx-
imately I horse-power for every
100-pound weight of hammer
head.
100 lb. Bradley hammer 3
200 lb. Bradley hammer 5
350 lb. Beaudry hammer 5
Bulldozers, Forming or
Bending Machines
Width Head Movement Horse-power
29 in. 14 in. 5
34 in. 16 in. 7I
39 in. 16 in. 10
45 in. 18 in. 15
63 in. 20 in. 20
Bulldozers (ajax)
No. 3 5
No. 4 7I
No. 5 10
No. 6 15
No. 7 30
No. 9 40
No. 12 50
Bolt Headers (hot)
Size Horse-power
f-i^ in. S- 7I
1^2 in. 10-15
Upsetting Machlnes
2 in. 7^-10
3 in. 10 -IS
5 in. IS -20
6 in. 20 -30
POWER REQUIRED BY MACHINE TOOLS 439
Hot Nut Machines
Size Horse -power
^ f in. 5
f-i in. 72-10
i|-2 in. 10 -15
Hyd. Wheel Peess
Size Horse-power
100 tons 5
200-300 tons 7 1
400 tons 10
600 tons 15
Bending and Straightening
Rolls
Width Thickness H.P.
4- 6 in. tV- I 5
6 in. i^- f 5-15
8 in. I 25
10 in. i|-i^ 35-50
24 in. I 50
Flue Machines
No. of Flues Horse-
Capacity power
Flue Rattler 250-300 20-30
Flue Cutter 2-3
Flue Welder 2-3
Notching Press (sheet-iron)
Dia. Punch Thickness Horse-power
f in. i I
i- f in. ^-1 2- 3
f in. I 3-5
l-i in. ^-f 5
1 in. I 7§
li in. I 72-10
if in. I 10 -15
2 in. I 10 -15
2i in. i^ 15 -25
Multiple Punch
4 holes I dia. | plate 7^-10
Shears
Horse-power
Gap Width Cut i Iron Cut J Iron
30-42 in. 3 5
56-60 in. 4 75
72--96 in. 5 10
Bolt shears 7^
Double angle shears 10
Rotary bevel shears 7I
Plate Shears
Metal CutperMin. Stroke H.P.
I X 24 in. 35 3 in. 10
1 X 24 in. 20 3 in. 15
2 X 14 in. 15 4i in. 30
I X 42 in. 20 4 in. 20
i| X 42 in. 15 4^ in. 60
ij X 54 in. 18 6 in. 75
i^ X 72 in. 20 5^ in. 10
ijxiooin. 10-12 72 in. 75
Lever Shears
Metal Cut Horse-power
1 X I in. 5
i^ X i| in. 7§
2 X 2 in. 10
6x1 in. 10
2I X 2I in. 10
I X 7 in. 15
2|x2fin. 15
1^x8 in. 20
3I X 3I in. 20
4I round 30
Motors Usually Employed
FOR Cranes and Hoists
Hoist
Capacity Speed H.P.
tons ft. per min.
5 25 15
50 25
10 30 25
40 40
15 20 25
20 15 25
25 10 25
IS 33
30 14 33
5 aux. 50 25
10 aux. 25 25
50 10 40
5 aux. 50 25
10 aux. 25 25
Bridge Trolley
Capacity Span H.P. H.P.
tons ft.
5 60 20 3
10 80 25 3
15 80 25 5
20 80 25 5
25 80 25 5
30 80 33 7h
35 80 40 75-10
440
HORSE-POWER, BELTS AND SHAFTING
POWER REQUIRED FOR
Band Saws
Max. width
of Saw H.P.
h
I 3
2-1^ 3-5
2I 10
3I 15
Dia. Wheel
30 in.
34 in.
36-38 in.
40-42 in.
40-42 in.
40-42 in.
Cut Off Saws
Dia. Saw No. of Saws H.P.
12-14 I 3
16 I 5
16 2 7^-10
30 I 72
Circular Rip Saws
14
I
5
16
I
7-
24
I
10
36
I
15
Timber Sizers
Capacity No. Heads H.P.
30 X 20 in. 4 50
20 X 20 in. 4 50
30 X 10 in. 4 40
20 X 16 in. 4 40
Size
30 X 6 in.
24 X 6 in.
30 X 8 in.
26 X 8 in.
24 X 6 in.
16x6 in.
24 X 8 in.
30 X 8 in.
Shapers, i-
Borers . . .
Surfacers
No. Heads H.P.
1-2
1-2
2
15-20 I s
15-20 \^l
30 %
30 Jk
5-7|l|
5- 7^ ^
^° Pa
10 J -^J
Horse-power
3-5
5-7i
Planers, Matchers and
Flooring Machines
Size Heads Horse-power
9 X 8 in. 4-5 30
19 X 8 in. 4-s 30
24 X 8 in. 4-5 40
•2 sp
PLANING-MILL EQUIPMENT
Size Heads Horse-power
30 X 8 in. 4-5 40
24X 12 in. 4-5 40
30x12 in. 4-5 40
Outside Moulders
Capacity No. Heads Horse-power
4 X 4 in. 1-2 5
4x4 in.. 3-4 7^
6 X 4 in. 1-2 5
6 X 4 in. 3-4 71
8 X 4 in. 4 10
10 X 4 in. 4 15
12 X 5 in. 4 20
14 X 6 in. 4 20
Inside Moulders
8x4 in. 4 15
10 X 4 in. 4' 15
10 X 6 in 4-5 20-30
15 X 4 in. 4-5 20-30
Jointers
S-12 in.
16-24 in.
30-36 in.
Tenoning Machines
No. Heads
5^ X 14 in. I 3-5
5|xi5in. 2 5
23 X 9 in. 2 7I
54 X 4§ in. 4-8 10 -IS
78 X 4^ in. 4-8 10 -15
Gainers 7j-io -15
Belt Sanders
Width of Belt Horse-power
6-14 in. 2-3
18 in. 5
Column Arm
Length of
Arm
4-10 ft.
Dia. of
Disks
Horse-power
8 in. 3
Drum Sanders
Length of Drum Horse-power
30 in.
36 in.
42-48 in.
54-60 in.
72-84 in.
7h
10
IS
20
30
POWER REQUIRED FOR MACHINE TOOLS 441
Group Driving of Machines
There are many shops where group driving will be found more
desirable than the use of individual motors, both as to first cost
and maintenance. This is particularly true where the machines
are comparatively small and run intermittently, as the cost of
motors will be much less.
Friction load of 2^ to 3-inch shafting, with bearings 8 to 10 feet
and running at 150 to 200 revolutions per minute, is about i horse-
power for ever}^ 30 feet of shafting. This includes the friction of
countershafts of the machines driven by it.
In group driving it is usually perfectly safe to select a motor
having a rated capacity of from 25 to 30 per cent, of the total power
required for the machines in the group.
Power Required for Punching and Shearing
Experiments tend to show that with steel plates of 60,000 pounds
tensile strength, the metal is all sheared when the punch has passed
^ through the plate. The following formula by L. R. Pomeroy takes
this into account and also allows the motor and efficiency of 80 per
cent, and the punching machine 75 per cent.
When T = FuU thickness of plate.
D = Diameter of hole punched.
N = Number of holes punched per minute.
P = Horse-power required to drive machine.
'nxDXN
3-78
Taking a |-inch hole in a ^-inch plate, the power required to
punch 30 per minute would be
iXiX3o 3.75 , ^ ,
r-^^ = - — r or about I horse-power.
3-78 3-78
Pressure required for shearing = Length of cut X thickness in
inches X shearing strength of material. Dies with "shear" reduce
this J to ^.
Power Required to Remove Metal
The power required to remove metal depends on the amount of
metal removed per minute and the nature of the cutting tool. With
a cutting angle of 75 to 80 degrees, tests show that for mild steel
of 40-point carbon one horse-power will remove 1.5 cubic inches of
metal per minute.
For average conditions and with tools as ordinarily used, tests
show that to remove one cubic inch of metal per min. requires the
amount of power shown in the table.
442 HORSE-POWER, BELTS AND SHAFTING
Brass and similar alloys 0.2 to 0.3 H.P.
Cast iron 0.3 to 0.5 "
Wrought iron ) ^ u
Mild steel (0.30% to 0.40% carbon) . . )
Hard steel (0.50% carbon) i.oo to 1.25 "
Very hard tire steel 1.50 "
Two important factors enter into the problem of power for driving
machines. These are the Time Factor and the Load Factor.
Time Factor =
Load Factor =
Actual Cutting Time
Total Time to Complete Operation
Average Daily Load
Full Load Rating of Motor
Many tests give the following load factors:
The average load factor for motors driving lathes is from 10
to 25 per cent. On some special macliines, as driving wheel and
car wheel lathes, the cuts are all heavy, which increases the average
load factor to from 30 to 40 per cent.
For extension boring mills, 5 horse-power motors are used to move
the housings on from 10 feet to 16 feet mills, 7I horse-power for
from 14 feet to 20 feet mills and 10 horse-power for from 16 feet to
24 feet mills. The load factor of the driving motor on boring mills
averages from 10 to 25 per cent.
The load factor of motor-driven drills is about 40 per cent, when
the larger drills applicable thereto are used. If the smaller drills
are used the load factor averages 25 per cent, and lower.
For the average milling operations the load factor averages from
10 to 25 per cent. On slab milling machines where large quantities
of metal are removed it will average from 30 to 40 per cent.
The work on this class of machinery is usually light and much
time is required in making adjustments. Hence the load factor is
rarely higher than 20 per cent.
On planers the load factor averages between 15 and 20 per cent.
The motor must be large enough to reverse the table quickly, yet
this peak load occurs for such short intervals that it does not in-
crease the average load per cycle very much.
The work done on shapers is of a varying character. With light
work the load factor will not exceed from 15 to 20 per cent.; with
heavy work, the load factor will be as high as 40 per cent.
The conditions with slotters are similar to those on shapers.
Horse-Power to Drive Machines
Extensive experiments by L. R. Pomeroy show that the horse-
power required equals the Feed per rev. or stroke X Depth of
POWER REQUIRED TO REMOVE METAL 443
cut in inches X Cutting speed in feet per minute X 12 X Number
of tools cutting X a Constant which depends on the material. This
checks up fairly well with actual motor tests. The constants given
are:
Cast iron 0.35 to 0.5
Wrought iron or soft steel 0.45 to 0.7
Locomotive driving wheel tires 0.70 to i. 00
Very hard steel i-oo to i.io
Handhng this in another way, Charles Robbins of the Westing-
house Electric & IManufacturing Co. gives: The horse-power =
Cubic inches removed per minute X a Constant. These constants
are:
Brass and similar alloys 0.2 to 0.3
Cast iron 0.3 to 0.5
Wrought iron 0.6
Mild steel (0.30 to 0.40 carbon) 0.6
Hard steel (0.50 carbon) i.oo to 1.25
Very hard tire steel 1.50
These represent average conditions with the cutting tools ordinarily
used.
A brief summary of the studies by Mr. Robbins gives interesting
data on various machines. These give factors as follows:
Time
Factor
Load
Factor
44%
41
54
50
55
27%
Radial drilline' machine
10
Portable millinsf machine
55
Portable slottinsf machine
12
Planers
L. R. Pomeroy also gives a method of determining the horse-power
required by the belt used to drive the machine. The formula is:
Hp. = Thickness of belt in inches X Width of belt in inches X
Diameter of pulley in inches X Revolutions per minute X
Constant for kind of belt.
These constants are:
Leather belt 0.0062 to 0.0098
Cotton belt 0.0036 to 0.0068
Rubber belt 0.0050 to 0.0082
STEEL AND OTHER METALS
HEAT TREATMENT OF STEEL
The theory of the heat treatment of steel rests upon the influence
of the rate of cooling on certain molecular changes in structure occur-
ring at different temperatures in the solid state. These changes are
of two classes, critical and progressive; the former occur periodically
between certain narrow temperature limits, while the latter proceed
gradually with the rise in temperature, each change producing alter-
ations in the physical characteristics. By controlling the rate of
cooling, these changes can be given a permanent set, and the physical
characteristics can thus be made different from those in the metal
in its normal state.
The highest temperature that it is safe to submit a steel to for
heat-treating is governed by the chemical composition of the steel.
Pure carbon steel should be raised to about 1650 degrees Fahr.,
while some of the high-grade alloy steels may safely be raised to 1750
degrees Fahr., and the high-speed steels may be raised to just below
the melting point, usually from 2000 to 2150 degrees Fahr. It is
necessary to raise the metal to these points so that the active cooling
process will have the desired effect of checking the crystallization of
the structure.
Methods of Heating
Furnaces using solid fuel such as coal, coke, charcoal, etc., are the
most numerous and have been used the longest. These furnaces
consist of a grate to place the fuel on, an arch to reflect the heat and
a plate to put the pieces on. The plate should be so arranged that
the flames will not strike the pieces to be heated, and for that reason
some use cast-iron or clay retorts which are open on the side toward
the doors of the furnace.
Liquid fuel furnaces, which have open fires and which use liquid
fuels, are not' very numerous at present, but their use is increasing,
owing to the ease with which the fire is handled and the cleanlmess
as compared with a coal, coke or charcoal fire.
Crude oil and kerosene are the fuels generally used in these fur-
naces, owing to their cheapness and the fact that they can be easily
obtained. These fuels are usually stored in a tank near the furnaces
and are pumped to them or flow by force of gravity.
Heating in Liquids
Furnaces using liquid for heating have a receptacle to hold the
liquid, w^hich k heated by coal, oil, gas or any other economical
means; the liquid is kept at the highest temperature to which the
piece should be heated. The piece should be heated slowly in an
ordinary furnace to about 800 degrees, after which it should b^
THE HARDENING BATH 445
immersed in the liquid bath and kept there long enough to attain the
temperature of the bath and then removed to be annealed or hardened.
The bath usually consists of lead, although antimony, cyanate of
potassium, chloride of barium, a mixture of chloride of barium and
chloride of potassium in the proportion of 3 to 2, mercury, common
salt and metallic salts have been successfully used.
This method gives good results, as no portion of the piece to be
treated can reach a temperature above that of the liquid bath; a
pyrometer attachment will indicate exactly when the piece has
arrived at that temperature, and its surface cannot be acted upon
chemically. The bath can be maintained easily at the proper tem-
perature and the entire process is under perfect control.
When lead is used it is liable to stick to the steel unless it is pure
and retard the cooling of the spots where it adheres. Impurities,
such as sulphur, are liable to be absorbed by the steel and thus afifect
its chemical composition. With high temperatures lead and cyanate
of potassium throw off poisonous vapors which make them prohibitive,
and even at comparatively low temperatures these vapors are detri-
mental to the health of the workmen in the hardening room. The
metallic salts, however, do not give off these poisonous vapors, and
are much better to use for this purpose, but many times the fumes
are unbearable.
Gas as Fuel
Furnaces using gaseous fuel are very numerous and are so con-
structed that they can use either natural gas, artificial gas, or pro-
ducer gas. They are very easy to regulate and if well built are
capable of maintaining a constant temperature within a wide range.
In first cost this style of furnace is greater than that of the solid
fuel furnaces, but where natural or producer gas is used the cost of
operating is so much less that the saving soon pays for the cost of
installation. Illuminating gas, however, is more expensive than the
solid fuels and is only used where high-grade work demands the best
results from heat treatment.
COOLING THE STEEL
Cooling apparatus is divided into two classes — baths for hard-
ening and the different appliances for annealing.
The baths for quenching are composed of a large variety of ma-
terials. Some of the more commonly used are as follows, being
arranged according to their intensity on 0.85 per cent, carbon steel:
Mercury; water with sulphuric acid added; nitrate of potassium; sal
ammoniac; common salt; carbonate of lime; carbonate of magnesia;
pure water; water containing soap, sugar, dextrine or alcohol; sweet
milk; various oils'; beef suet; tallow; wax. These baths, however,
do not act under all conditions with the same relative intensity, as
their conductivity and viscosity vary greatly with the temperature.
With the exception of the oils and some of the greases, the quench-
ing effect increases as the temperature of the bath lowers. Sperm
and linseed oils, however, at all temperatures between 32 and 250
degrees Fahr., act about the same as distilled water at 160 degrees.
44^ STEEL AND OTHER METALS
The baths for hardening which give the best results are those in
which some means are provided for keeping the Hquid at an even
temperature. Where but few pieces are to be quenched, or a con-
siderable time elapses between the quenching of pieces, the bath will
retain an atmospheric temperature from its own natural radiation.
Where a bath is in continuous use, for quenching a large number of
pieces throughout the day, some means must be provided to keep the
temperature of the bath at a low even temperature. The hot pieces
from the heating furnace will raise the temperature of the bath many
degrees, and the last piece quenched will not be nearly as hard as the
first.
Annealing
The appliances for annealing are as numerous as the baths for
quenching, and where a few years ago the ashes from the forge were
all that were considered necessary for properly annealing a piece of
steel, to-day many special preparations are being manufactured and
sold for^this purpose.
The more common materials used for annealing are powdered
charcoal, charred bone, charred leather, slacked lime, sawdust,
sand, fire clay, magnesia or refractory earth. The piece to be
annealed is usually packed in a cast-iron box, using some of these
materials or combinations of them for the packing, the whole is then
heated in a furnace to the proper temperature and set aside, with
the cover left on, to cool gradually to the atmospheric temperature.
For certain grades of steel these materials give good results; but
for all kinds of steels and for all grades of annealing the slow-cooling
furnace no doubt gives the best satisfaction, as the temperature can
be easily raised to the right point, kept there as long as necessary,
and then regulated to cool down as slowly as is desired. The gas,
oil or electric furnaces are the easiest to handle and regulate.
The Hardening Bath
In hardening steels the influence of the bath depends upon its
temperature, its mass and its nature; or to express this in another
way, upon its specific heat, its conductivity, its volatility and its
viscosity. With other things equal, the lower the temperature of
the bath, the quicker will the metal cool and the more pronounced
will be the hardening effect. Thus water at 60 degrees will make
steel harder than water at 150 degrees, and when the bath is in con-
stant use the first piece ^quenched will be harder than the tenth or
twentieth, owing to the rise in temperature of the bath. Therefore if
uniform results are to be obtained in using a water bath, it must
either be of a very large volume or kept cool by some mechanical
means. In other words, the bath must be maintained at a constant
temperature.
The mass of the bath can be made large so no great rise in tem-
perature is made by the continuous cooling of pieces, or it can be made
small and its rise in temperature used for hardening tools that are to
remain fairly soft, as, if this temperature is properly regulated, the
tool will not have to be re-heated and tempered later, and cracks and
fissures are not as liable to occur.
HEATING AND TEMPERING 447
Another way of arriving at the same results would be to use the
double bath for quenching, that is, to have one bath of some product
similar to salt which fuses at 575 degrees Fahr. Quench the piece
in that until it has reached its temperature, after which it can be
quenched in a cold bath or cooled in the air.
BATH FOR DRAWING TEMPER
A VERY good table from which to make up baths for drawing the
temper is as follows:
Composition of Bath Melting Point in * Color of Steel at
Lead and Tin degree F. Temperature Given
14 8 420 very faint yellow
15 8 430 faint yellow
16 8 440 light straw
17 8 450 straw
18.5 8 460 full straw
20 8 470 dark straw
24 8 480 old gold
28 8 490 brown
38 8 510 brown with purple spots
60 8 530 purple
96 8 550 deep purple
200 8 560 blue
BoUing linseed oil 600 dark blue
Melted lead 610 gray blue
These are used in a similar manner to the hardening baths, select-
ing the bath which gives the proper drawing temperature.
HIGH-SPEED STEELS
These steels are made by alloying tungsten and chromium or
molybdenum and chromium with steel. These compositions com-
pletely revolutionize the points of transformation. Chromium, which
has a tendency to raise the critical temperature, when added to a
tungsten steel, in the proportions of i or 2 per cent., reduces the
critical temperature to below that of the atmosphere. Tungsten
and molybdenum prolong the critical range of temperatures of the
steel on slow cooling so that it begins at about 1300 degrees Fahr.
and spreads out all the way down to 600 degrees.
These steels are heated to 1850 degrees for the molybdenum and
2200 degrees for the tungsten, and cooled moderately fast, usually in
and air blast, to give them the property known as "red-hardness."
This treatment prevents the critical changes altogether and pre-
serves the steel in what is known as the austenitic condition. The
austenitic condition is one of hardness and toughness.
One rule which has given good results in heat-treating these high-
speed steels is to heat slowly to 1500 degrees Fahr., then heat fast
to 2200 degrees; after which cool rapidly in an air blast to 1550
degrees; then cool either rapidly or slowly to the temperature of the
air. Others advocate cooling in crude oil.
448 STEEL AND OTHER METALS
CASE-HARDENING
Case-hardening, carbonizing, or, as it is called in Europe, "cemen-
tation," is largely used so that the outer shell can be made hard enough
to resist wear and the core of the piece can be left soft enough to with-
stand the shock strains to which it is subjected.
Several methods different from the old established one of packing
the metal in a box filled \vith some carbonizing material, and then
subjecting it to heat, have been devised in the last few years. Among
them might be mentioned the Harveyizing process which is especially
applicable to armor plate. The Harveyizing process uses a bed of
charcoal over the work, the plates being pressed up against it in a pit
or furnace and gas turned on so that the steel will be heated through
the charcoal, thus allowing the carbon to soak in from the top.
The result of the carbonizing operation is determined by five
factors, which are as follows: First, the nature of the steel; second,
the nature of the carbonizing material; third, the temperature of the
carbonizing furnace; fourth, the time the piece is submitted to the car-
bonizing process; fifth, the heat treatment which foUows carbonizing.
The nature of the steel has no influence on the speed of penetra-
tion of the carbon, but has an influence on the final result of the
operation.
If steel is used that has a carbon content up to 0.56 per cent., the
rate of penetration in carbonizing is constant; but the higher the
carbon content is, in the core, the more brittle it becomes by pro-
longed anneahng after carbonizing. Therefore it is necessary that
the carbon content should be low in the core, and for this reason a
preference is given to steels containing from 0.12 to 0.15 per cent,
of carbon for carbonizing or case-hardening purposes.
Table i. — Penetration of Carbon per Hour with
Different Alloys gpeed of Penc
Component of AUoys n/'^bTn^hK
0.5 per cent, manganese 0.043
i.o per cent, manganese 0.047
i.o per cent, chromium 0.039
2.0 per cent, chromium 0.043
2.0 per cent, nickel 0.028
5.0 per cent, nickel 0.020
0.5 per cent, tungsten ■. 0.035
1.0 per cent, tungsten 0.036
2.0 per cent, tungsten 0.047
0.5 per cent, silicon 0.024
1.0 per cent, silicon ; 0.020
2.0 per cent, silicon 0.016
5.0 per cent, sihcon 0.000
1.0 per cent, titanium 0.032
2.0 per cent, titanium , 0.028
1.0 per cent, molybdenum 0.036
2.0 per cent, molybdenum 0.043
1.0 per cent, alumimmi 0.016
3.0 per cent, aluminum 0.008
CASE HARDENING
449
The rate of penetration for ordinary carbonizing steel under the
same conditions would have been 0.035 inch. Thus it will be seen
that manganese, chromium, tungsten and molybdenum increase
the rate of penetration. These seem to exist in the state of a double
carbide and release a part of the cementite iron.
Nickel, silicon, titanium and aluminum retard the rate of penetra-
tion — 5 per cent, of silicon reducing it to zero — and these exist in
the state of solution in the iron.
The Carbonizing Materials
The nature of the carbonizing materials has an influence on the
speed of penetration and it is very essential that the materials be of
a known chemical composition as this is the only way to obtain like
results on the same steel at all times.
These materials or cements are manufactured in many special
and patented preparations. The following materials are used and
compounded in these preparations, but many of them give as good
results when used alone as when compounded with others in varying
percentages: Powdered bone; wood charcoal; charred sugar; charred
leather; cyanide of potassium; ferro-cyanide of potassium; bichro-
mate of potassium; animal black, acid cleaned. Prussiate of potash,
anthracite, mixture of barium carbonate, graphite, petroleum gas,
acetylene, horn, etc.
Wood charcoal is very largely used in carbonizing steels, but the
value of this material varies with the wood used, the method em-
ployed in making the charcoal, and other factors. Used alone it
gives the normal rate of penetration for the first hour, but after that
the rate gradually decreases until at eight hours it gives the lowest
rate of penetration of any of the carbonizing materials. The best
wood charcoal is that made from hickory.
Powdered charcoal and bone give good results as a carbonizing
material and are successfully used in carbonizing nickel-chrome steel
by packing in a cast-iron pot and keeping at a temperature of about
2000 degrees Fahr. for four hours, and then cooling slowly before
taking out of the pot or uncovering.
Table 2
Temperature
in Degrees
Fahrenheit
1300
1475
1650
1825
2000
Materials Used and Rate of Penetration in Inches
Charcoal 60 per
cent, -t- 40 per
cent, of Carbon-
ate of Borixim
0.020
0.088
0.128
0.177
Ferro-cyanide 66
per cent. + 34
per cent, of
Bichromate
Ferro-cyanide
Alone
0.033
0.069
0.128
0.177
0.020
0.079
0.128
0.198
Powdered Wood
Charcoal Alone
0.020
0.048
0.098
0.138
The speed of penetration caused by the action of different cements
at different temperatures for the same time, i.e., eight hours, is best
shown by Table 2.
450
STEEL AND OTHER METALS
The nature of the carbonizing material has a very pronounced
effect on the rate of carbonization, or the percentage of the carbon
content in the surface layer of the piece, or both.
Another Test of Penetration
At the same temperature.
1825 degrees Fahr., for different
lengths of time and with different cements, the rate of penetration
obtained was according to Table 3.
Eighty per cent, charcoal + 20 per cent, carbonate of barium,
40 per cent, charcoal + 60 per cent, carbonate of barium, ferro-
cyanide alone and 66 per cent, ferro-cyanide + 34 per cent, bichro-
mate were used with practically the same results for eight hours' time.
Table 3
Materials Used anx> Rate of Penetration in Inches
Length of
Time in
Hours
Carbon 60
per cent.+ 40
per cent, of
Carbonate
Ferro-cyan-
ide 66 per
cent.+ 34
per cent, of
Bichromate
Powdered
Wood
Charcoal
Alone
Charcoal and
Carbonate
of
Potassium
Unwashed
Animal
Black
I
2
4
6
8
0.031
0.039
0.047
0.078
O.I18
0.033
0.037
0.049
0.074
0.128
0.028
0.053
0.063
0.072
0.098
0.059
0.078
0.094
O.OII
0.138
0.035
0.059
0.088
0.106
0.128
Another set of tests was carried out for a longer period of time,
with other materials and at a uniform temperature of 1650 degrees
Fahr., with the results given in Table 4.
Table 4
Materxaxs Used and Rate of Penetration in Inches
Length of Time
in Hours
Charred
Leather
Ground Wood
Charcoal
Barium Carbonate
and Wood Charcoal
2
4
8
12
0.045
0.062
0.080
O.IIO
0.028
0.042
0.062
0.070
0.055
0.087
O.III
0.125
PROPERTIES OF STEEL
451
In the use of hydrocarbons, or gases, a fresh supply can be kept
flowing into the carbonizing receptacle and the time greatly reduced
for deep penetration with an appreciable reduction of time for the
shallow penetrations.
The constitution of a given steel is not the same in the hardened
as in the normal state, owing to the carbon not being in the same
state. In the annealed or normal steel it is in a free state, while in a
hardened steel it is in a state of solution which we may call marten-
site; and this contains more or less carbon according to the original
carbon content of the steel. The composition, and therefore the
mechanical properties, depend principally upon the carbon content,
the mechanical properties being changed slowly and gradually by an
increase in carbon.
This is best shown by Table 5 in which it will be seen that the
tensile strength and elastic limit gradually increased with the increase
in the percentage of carbon, both in the annealed and hardened state
Table 5. — Effect of Composition and Hardening on the
Strength
Case
Harden-
ing Steel
Very
Low
Carbon
Low
Carbon
Medium
Carbon
High
Carbon
Very
Carbon
Carbon
O.IO
0.09
0.19
0.016
0.025
0.14
0.05
0.33
0.023
0.052
0.23
0.15
0.45
0.091
0.062
0.52
0.18
0.35
0.021
0.043
0.60
O.IO
0.40
0.035
0.025
0.72
0.17
Manganese
Phosphorus
Sulphur
0.38
0.03
0.06
MECHANICAL PROPERTIES WHEN ANNEALED
Tensile Strength (in
pounds per square
inch)
Elastic Limit (in
pounds per square
inch)
Elongation (percent-
age in 4 inches) . . .
60,300
61,500
66,500
97,800
116,400
36,300
35,200
41,200
52,600
66,500
29
27
26
20
14
130,700
75,800
9
MECHANICAL PROPERTIES "WTIEN HARDENED
Tensile Strength (in
pounds per square
inch)
Elastic Limit (in
pounds per square
inch)
Elongation (percent-
age in 4 inches) . . .
66,400
73,100
99,400
132,100
153,400
40,300
39,600
54,000
81,400
102,100
24
22
14
9
4
180,100
105,500
o
452 STEEL AND OTHER METALS
while the elongation gradually decreased. These tests were made
with bar i inch in diameter and 4 inches in length. It will also be
seen that there was considerable change in the steels which were too
low in carbon to be made so hard that they could not be filed. The
reduction in elongation when the test bars were heated and quenched
show that the metal was harder than when in the annealed state.
Selecting the Proper Temperature for Quenching
A hardening process that will produce a steel that is as homo-
geneous as possible is always sought for in practice. This is easily
obtained in a high-carbon steel and especially if it contains 0.85 per
cent, carbon, by passing the recalescent point before quenching.
The desired homogeneity is not so easily obtained, however, in the
low-carbon steels as they have several points of transformation. If
these are quenched at a point a little above the lowest point of trans-
formation the carbon will pass into solution, but the solution is not
homogeneous. To obtain this result it is necessary that the quench-
ing be done from a Httle above the highest point of transformation..
This is higher in the low- than in the high-carbon steels. In practice
this calls for a quenching of the low-carbon steels as about 1650
degrees Fahr., while a high-carbon steel should be quenched at about
1450 degrees.
Testing Pyrometers
P)Tometers can be tested by placing some common salt in an
iron box and heating until it melts. Put the pyrometer in the molten
salt and, if correct, it will register 1441 degrees Fahr.
A Table of Fahrenheit and Centigrade thermometer scales is given
on page 455.
Test of Hardness
The hardness of metals, particularly of steels which are heat
treated, is now tested with either the Shore Scleroscope or the Brin-
nell Ball method.
THE BRINNELL TEST
The Briimell method of testing consists of forcing a hardened steel
ball of given dimension into the metal to be tested under a given
pressure. The diameter of the impression made is read with a gradu-
ated microscope and the hardness found by consulting the table
below. In this the ball is 10 millimeters in diameter. If, with a
pressure of 3000 kilograms as indicated by the testing machine, the
diameter of the depression is 3 millimeters, the hardness number is
418. Dividing this by 6 gives practicall}^ 70, as shown under the
second column. According to this table, a pressure of only 500
kilograms will give a direct reading which is about the same as that
of the Scleroscope. The standard pressure however is 3000 kilograms.
THE BRINNELL METHOD
453
Hardness
Numeral
Pressure.
Kilograms
1
1
0000000000000000>0000
s S; s^ 8>c^c^§ o?<^ c2 eg s j:^ ^ i^ i R^g
Diameter
of Impres-
sion, Milli-
meters
I00"i0>o0to0>^0io0ir50to0io0vo
Hardness
Numeral
Pressure,
Kilograms
a
tOfOP^<^^l-<Ml-!o■dd^d^ 6>od 00 r^ i>- t^vO -o" O
1
too i^^MOOvO ThHOO^ tKn ot^i^fow Or^
Tf^rOcO^O'N'NMNMMMMOOOOOaOv
Diameter
of Impres-
sion, Milli-
meters
u-)Oii^O'00»^0»^0»oO»nO'oO»nOio
0Oi-iMM0»rotO^tir) ir>vO O t~. t^OO 00 O Ov
Hardness
Numeral
Pressure,
Kilograms
8
q q o q ^■o "^ 9 '^ "1" '^ 1 't'^ "^ ^ "^ '1' "? '1'
o6 t-^vd lA'j-roMpiwddv dvod j-^ t>.o lo to -4 -^
1
ci p. M M o O Ov ooo 00 X i< Xvo <i xn^^n^^
W<N<N<NM<NI-,MI-IMHHHHMMHHHM
Diameter
of Impres-
sion, Milli-
meters
ioOuoOvoOir.O»«OtoOioO >o 0 »o O 1^
Hardness
Numeral
Pressure,
Kilograms
a
KLo VO VO VO C^ ir, lO iS >o Co ^ ^^ ^ 4 4 ■* 4 ^0
1
oOMr^iOTtMOfNMMN fOO r^ t> N »ooO h to
M o 00 t^O vo rt- to <N M O ooo i-O vo >^ "* 'f CO
^rftOtOtOtOcocotococONMMMNNMMCN
Diameter
of Impres-
sion, Milli-
meters
tOtOCOcocococototototototococotOtococOtO
Hardness
Numeral
Pressure,
Kilograms
I
'S. S, ?^ ?> ^ 2" ;? ^ ^ 8 S S<^S c2>cg 5: ^ ?1
1
vO00t>.t^M -^totot^t^QooiOP) NTTjr^O -^O
^OviOMOO Tt-MOO >OM O f^tncOM Ov t->0 •* to
ooo 00 00 r- t^ t^« vovO^O inminin-t^^^-*
Diameter
of Impres-
sion, Milli-
meters
ioO«oO>AOioOu^OioOinOioOioOio
00>HM<se<totO'*-*'o loo vo t^ r^oo oo O O
<N<NMMNMNC<(NWNMC<M«C<P)<»M<S
454
STEEL AND OTHER METALS
SCLEROSCOPE READING
In the Shore Scleroscope, a miniature drop hammer tup falls from
a fixed height to the surface of the metal being tested. The height
of the rebound indicates the hardness on an arbitrary scale which
has 115 divisions, these meeting all usual requirements. This
method can be applied to any material which will take a permanent
set under impact. For, no matter how hard the material, the falling
weight, weighing about 40 grains, makes a dent which can be seen
with a glass.
The following table shows the readings which will be obtained on
the Scleroscope for the materials indicated, this giving the compara-
tive hardness of thte materials.
Scleroscope Hardness Scale
Metal
Lead — cast
Babbitt
Gold
Silver
Brass — cast
Pure Tin — cast
Brass — drawn
Bismuth — cast
Platinum
Copper — cast
Zinc — cast
Iron — pure
Mild steel, 0.15 carbon
Nickel Anode — cast
Iron, gray — cast
Iron, gray — chilled
Steel, tool, 1% carbon
Steel, tool, 1.65% carbon . . .
Vanadium steel
Chrome — Nickel
Chrome — Nickel, hardened
Steel, high speed, hardened .
Steel, carbon, tool, hardened
Hammered
3- 7
20- 30
12
20-
45
17
14-
20
20
25-
30
30- 45
55
50-
90
40-
50
60-
95
70-105
90-110
Note. — These figures vary with the composition and density
of the metals. They are about i those of the Brinnell test for equal
hardness, varying somewhat with the kind of metal.
ALLOYS FOR COINAGE
455
Fahrenheit and Centigrade Thermometer Scales
F
C
F
C
F
C
F
C
F
C
- 40
- 40.
70
21. 1
185
85.
950
Sio.
2100
1149.
-35
- 37-2
75
23-9
190
87.8
1000
537.8
2150
1176.5
-30
- 34-4
80
26.7
195
90.6
1050
565-5
2200
1204.
- 25
- 31-7
85
29.4
200
93-3
1 100
593-
2250
1232.
— 20
- 28.9
90
32.2
205
9b.i
1150
621.
2300
1260,
- 15
- 26.1
95
35-
210
98.9
1200
648.5
2350
1287.5
— 10
- 23.3
100
37.8
212
100.
1250
676.5
2400
1315-5
- 5
— 20.6
105
40.6
215
101.7
1300
704.
2450
1343-
0
-17.8
no
43-3
225
107.2
1350
732.
2500
1371-
+ 5
- 15-
115
46.1
250
121. 2
1400
760.
2550
1399-
10
— 12.2
120
48.9
300
148,9
1450
788.
2600
1426.5
15
- 9.4
125
51-7
350
176.7
1500
816.
2650
1455.
20
- 6.7
130
54.4
400
204.4
1550
844.
2700
1483.
25
- 3-9
135
57.2
450
232.2
1600
872.
2750
1510.
30
— I.I
140
60.
500
260.
1650
899.
2800
1537.5
32
0
145
62.8
550
287.8
1700
926.
2850
1565.
35
+ 1-7
150
65.6
600
315-6
1750
954.
2900
1593-
40
4.4
155
68.3
650
343-3
1800
982.
2950
1621.
45
7.2
160
71. 1
700
37I-I
1850
lOIO.
3000
1648.5
50
10.
165
73-9
750
398.9
1900
1038.
3050
1676.
55
12.8
170
75.7
800
426.7
1950
1065.5
3100
1705.
60
15.6
175
79-4
850
454-4
2000
1093.
3150
1732.
65
18.3
180
82.2
900
482.2
2050
1121.
3200
1760.
To convert Fahrenheit into Centigrade: Subtract 32 from Fahren-
heit, divide remainder by 9 and multiply by 5.
Example: 212 Fahr.
32
'°- • 9 = 20. 20 X 5 = 100.
180
180
Ans
212 Fahr. = 100 Cent.
Centigrade to Fahrenheit: Divide by 5, multiply by 9 and add 32.
Example: 260 Cent. -7-5 = 52. 52 X 9 = 468 -f- 32 ^ "
Ans, 260 Cent. = 500 Fahr.
500 Fahr.
Alloys for Coinage
Other
Gold
Copper
SUver
Constitu-
ents
Remarks
Gold coin
91.66
8.33
British standard.
" "
90.0
10. 0
—
—
"Latin Union" and American.
1-33
82.73
15-93
—
Roman, Septimus Severus,
265 A.D.
" "
40.35
19.63
40.02
—
Early British B.C. 50.
Silver coin
0.1
7-1
92.05
Lead 0.2
RomanB.C. ^i, almost same
as British silver coin.
7-5
92.5
—
British standard.
4S6
STEEL AND OTHER METALS
Composition of Bronzes (Navy Department)
White Metal: parts
Tin 7.6
Copper 2.3
Zinc 83,3
Antimony 3.8
Lead 3.0
Hard Bronze for Piston Rings:
Tin 22.0
Copper 78.0
Bearings — Wearing Surfaces, etc. :
Copper 6
Tin I
Zinc : \
Naval Brass:
Copper 62.0
Tin i.o
Zinc 37.0
Brazing Metal:
Copper 85.0
Zinc 15.0
Antifriction Metal :
Copper — (best refined) 3.7
Banca tin 88.8
Regulus of antimony 7.5
Well fluxed with borax and rosin in mixing.
Bearing Metal — (Pennsylvania Railroad) :
Copper 77.0
Tin 8.0
Lead 15.0
Bearing Metal
In the Journal of the Franklin Institute G. H. Clamer states that
13 parts antimony and 8j parts lead make an excellent bearing
metal, these being exactly the proportions which give a homogeneous
structure. For heavier duty tin should be added.
Bismuth Alloys (Fusible Metals)
Bismuth
Lead
Tin
Cadmium
Melting
Point
C
Newton's alloys . . .
50.0
31-25
i8-75
—
95
Rose's " ...
50.0
28.10
24.64
—
100
Darcet's " ...
50.0
25.00
25.00
—
93
Wood's " ...
50.0
24.00
14.00
12.00
66-71
Lipowitz's "
50.0
27.00
13.00
10.00
60
BRASS AND OTHER ALLOYS
Alloys
457
Copper
Tin
Lead
Zinc
Nickel
Anti-
mony
Babbitt
8.
Q2.
4-
Very hard.
Bell metal ....
76.5
74.8
23-5
25.2
"Big Ben,"
Westminster,
Brass
63-72
27-34
Typical brass.
" wire ....
70. 2Q
0.17
29.26
Britannia
1.46
90.62
7.81
Birmingham
sheet.
Bronze
95
4.
I.
British coinage.
80-90
12-18
7-
Heavy bearings.
German silver . .
60
20.
20
Nickel varies.
Gun metal ....
91
9.
Cannons.
Mannheim gold
80-88
20-12
Muntz metal . .
60-62
38-40
Ship sheathing.
Packf ong
43.8
40.6
Chinese alloy.
Shot metal ....
99.6
15.6
Trace of arsenic.
Speculum
70.24
29,11
trace
Telescope mir-
Type metal ....
2.0
10.
70
18.
3-2
82
14.
Stereotyping.
White metal . .
6.
82.
12.
For bearings.
Brass Alloys
Strictly, a brass is a copper-zinc alloy containing one-third zinc
and two- thirds copper; whereas a bronze is a copper- tin alloy con-
taining approximately 10 per cent, tin and 90 per cent, copper. The
old-style gun metal contained from 90 to 92 per cent, copper and
from 8 to 10 per cent. tin. Lead is frequently added to both these
classes of alloy to make them machine more easily, and both tin and
zinc are commonly used in the same alloy, so that today we have a
series of copper-tin-zinc alloys of almost infinite variety. In all cases
in the useful alloys of this class, however, there is present more than
50 per cent, copper.
In most of the modern alloys tin is depended upon to give strength
and zinc to cheapen the mixture. Some of the old-style gun metals
contained as much as 16 per cent, tin and 84 per cent, copper, but
such metals were brittle and hard. The common yellow brass
employed by plumbers in making ordinary valves and fittings may
be considered as composed of approximately 16 pounds copper, 8
pounds zinc, and ^ pound lead. It will be noticed that this consists
of approximately one-third zinc and two-thirds copper, with a little
lead added to improve the machining quahties. For the making of
high-grade casting ingots or new metal should be used in all cases.
In making a brass the copper should be melted first and the zinc
added, care being taken not to let the temperature rise too high, for
if it does the zinc will ignite and burn. The lead is added last and
the metal thoroughly stirred.
458
STEEL AND OTHER METALS
Properties of Metals
Metal
Aluminum . .
Antimony . .
Bismuth ....
Brass, cast . .
Bronze
Chromium . .
Cobalt
Copper
Gold
Iridium ....
Iron, cast . . .
Iron, wrought
Lead
Manganese .
Mercury . . .
Nickel
Platinum . . .
Silver
Steel — cast
Steel — rolled
Tin
Tungsten . . .
Vanadium. . .
Zinc
Melting
Point
1217
I166
518
1692
1692
2750
2714
1981
1945
4172
2700
2920
621
2237
-36
2646
3191
1761
2450
2600
449
5430
3146
7S6
Wt. per
Cu. In.
0924
2424
354
3029
319
2457
307
322
6979
8099
26
278
41
289
4909
3179
7769
3805
28
2833
2634
69
1987
245
Wt. per
Cu. Ft.
159-63
418.86
611.76
523-2
550.
429-49
530.6
556.
1206.05
1400.
450-
480.13
710.
499.4
848.35
549-34
1342.13
657-33
481.2
489.6
45 5 -08
1192.31
343-34
430-
Tensile
Strength
24,000
36,000
36,000
20,000
16,500
50,000
3,000
40,000
50,000
65,000
4,600
7,500
Specific
Gravity
2.56
6.71
9-83
8.393
8.83
6.8
8.5
8.9
19.32
22.42
7.21
7-7
11.37
8.
13-59
8.8
21.5
10.53
7.81
7-854
7-29
19.10
5-50
6.86
Al.
Sb.
Bi.
Cr.
Co.
Cu.
Au.
Ir.
Fe.
Fe.
Pb.
Mn.
Hg.
Ni.
Pt.
Ag.
Sn.
W.
V.
Zn.
Shrinkage of Castings
Aluminum — pure 2031 inch per foot
Nickel Alloy 1875 "
Special Alloy 1718 "
Iron, Small Cylinders 0625 "
" Pipes 125 "
" Girders and Beams 100 ''
" Large Cylinders, Contraction of Diameter
at Top. ^ 0625 "
" Large Cylinders, Contraction of Diameter
at Bottom 083 "
" Large Cylinders, Contraction of Length .. . .094 "
Brass — Thin 167 "
" Thick ; - .150 "
Copper 1875 "
Bismuth 1563 ''
Lead 3125 "
Zinc 3125 "
ALUMINUM 45Q
Aluminum
Can be melted in ordinary plumbago crucibles the same as brass
and will not absorb silicon or carbon to injure it unless overheated.
Melts at 1 21 7 degrees Fahr. or 625 Cent. Becomes granular and
easily broken at about 1000 Fahr.
Shrinkage of pure aluminum 2031" per foot
Nickel Aluminum Casting Alloy 1875" " "
Special Casting Alloy 1718" " "
The most used alloys have a strength of about 20,000 pounds to
square inch at a weight of one third that of brass.
Iron or sand molds can be used and should be poured as cool as
it will run to avoid blowholes.
Burnishing. — Use a bloodstone or steel burnisher, with mixture
of melted vaseline and kerosene oil or two tablespoonfuls of ground
borax, dissolved in a quart of hot water and a few drops of ammonia
added.
Frosting. — Clean with benzine. Dip in strong solution of caustic
soda or potash, then in solution of undiluted nitric acid. Wash
thoroughly in water and dry in hot sawdust.
Polishing. — Any good metal polish that will not scratch will clean
aluminum. One that is recommended is made of
Stearic Acid — One part ]
Fuller's Earth — One part j- Grind fine and mix very well.
Rotten Stone — Six parts J
Castings are cleaned with a brass scratch brush, run at a high
speed. Sand blasting is also used both alone and before scratch
brushing.
Spinning. — A high speed, about 4000 feet per minute, is best for
spinning. This means that for work 5 to 8 inches in diameter,
2800 to 2600 revolutions per minute is good, while for smaller work
of 4 inches this would go up to 3200 r.p.m.
Turning. — Use a tool with shearing edge similar to a wood-
cutting tool as they clear themselves better. Use kerosene or water
as a lubricant, or if a bright cut is wanted use benzine. For drawing
on a press use vaseline.
Soldering. — See page 92.
U. S. Armary Method of Bluing Steel. — Have work clean and free
from grease. Take 10 parts of nitre and i part of manganese. Heat
in this mixture to from 700 to 800 degrees F. and quench in oil.
STEAM HAMMERS AND DROP FORGING
While it is impossible to accurately rate the capacity of steam
hammers \\nth respect to the size of work they should handle, on
account of the greatly varying conditions, a few notes from the
experience of the Bement works of the Niles-Bement-Pond Company
will be of service.
For making an occasional forging of a given size, a smaller hammer
may be used than if we are manufacturing this same piece in large
quantities. If we have a 6-inch piece to forge, such as a pinion or
a short shaft, a hammer of about iioo pounds capacity would answer
very nicely. But should the general work be as large as this, it
would be very much better to use a 1500-pound hammer. _ If, on the
other hand, we wish to forge 6-inch axles economically, it would be
necessary to use a 7000- or Sooo-pound hammer. The following
table will be found convenient for reference for the proper size of
hammer to be used on different classes of general blacksmith work,
although it will be understood that it is necessary to modify these
to suit conditions, as has already been indicated.
Diameter of Stock Size of Hammer
3A Inches 250 to 350 pounds
4 Inches 35o to 600 pounds
4i Inches 600 to 800 pounds
5 Inches 800 to 1000 pounds
6 Inches i i°o to 1500 pounds
Steam hammers are always rated by the weight of the rani, and the
attached parts, which include the piston and rod, nothing being added
on account of the steam pressure behind the piston. This makes it
a little difficult to compare them with plain drop or tilting hammers,
which are also rated in the same way.
Steam hammers are usually operated at pressures varying from
75 to 100 pounds of steam per square inch, and may also be operated
by compressed air at about the same pressures. It is cheaper, how-
ever, in the case of compressed air to use pressures from 60 to 80
pounds instead of going higher.
In figuring on the boiler capacity for steam hammers, there are
several things to be considered, and it depends upon the number of
hammers in use and the service required. It will vary from one
boiler horse-power for each 100 pounds of falling weight up to three
horse-power for the same weight, according to the service expected.
In a shop where a number of steam hammers are being used, it is
usually safe to count on the lower boiler capacity given, as it is
practically safe to say that all of the hammers are never in use at
the same time. In a shop with a single hammer, on the other hand,
and especially where hard service is expected, it is necessary to allow
the larger boiler capacity as there is no reserve to be drawn on, due
to part of the hammers being idle, as in the other case.
460
DROP FORGING DIES
461
DRAFT IN DROP FORGING DIES
In sinking dies for drop forging, it is important that the draft at
the sides of the impression should be made as Httle as possible to
avoid heavy cuts in the machining operations. It is equally im-
portant that the draft be sufficient to allow the forging to be easily
withdrawn from the die, else production under the hammer will be
hampered. The standard draft (or draw) for most dies is 7 degrees
from the perpendicular, but other angles are used in special cases
and sometimes two or three different angles of draft are used in the
same die at different parts of the impression.
Figure i shows the plan and side elevation of a lower die where
three angles of draft are advisable. The shoulders A and B are
EK
^|a f
BP
1 ^
ef[)
2 a ""
c „
m
70
Fig. I. — Example of Draft in Drop Forging Dies
places where the metal is likely to hug on account of the contraction
of the hot m.etal along the part marked C, which is of comparatively
small cross-section and will cool rapidly. These shoulders are given
an angle of 9 degrees. The inserted tool-steel plug D, is another
place where metal is likely to hug badly. It is usual to give such
plugs 12 and even 15 degrees of draft on each side. Moreover, the
tendency of plugs to get "jumped up," hammered over and badly
heat checked is much reduced if they are given a big draft. The
part marked E is semicircular and will draw easily. The end of E
at F is a part of a sphere. All other sides of the impression are given
7 degrees draft. If the die is smooth and regular the forging will
draw easily.
AW. impressions are laid out to one-eighth inch to the foot shrink
rule. This allows for a shrinkage of about o.oio inch to the inch.
The same shrinkage is allowed in the thickness of forgings. For
example: A forging is to be 2 inches thick with half the thickness in
each die. The depth of impressions will be i.oio inch in each die.
In laying out the impression on the face of the die, allowance has
been made for shrinkage in length, thickness and breadth of forging,
and, in addition, for the draft on the sides. In complex dies where
there are many different depths and offsets on the face of the die, the
die sinker has to keep all these points constantly in mind while laying
out or run the risk of spoiling the whole job.
A Table of Draft Dimensions
The allowance for 7-degree draft is easy to remember, being almost
exactly 3V inch at the face of the die for each \ inch of depth. Table
I has been calculated to give the allowances in thousandths of an
462
STEAM HAMMERS AND DROP FORCINGS
inch on actual depth, as measured with an ordinary depth gage.
It is not usual in marking out to work closer than -^^ inch, but the
Table i. — Allowance in Thousandths of an Inch at Face of
Dle for Standard Angles of Draft and Various Depths
OF Impression
Depths in
St
.^NDARD Draft Angles m Degrees
Inches
5 Degrees
7 Degrees
9 Degrees
12 Degrees
Inch
Inch
Inch
Inch
O.OII
0.015
0.020
0.027
0.022
0.033
0.044
0.031
0.046
0.061
0.040
0.059
0.079
O.OS3
0.080
0.106
o.oss
0.077
0.099
0.133
0.066
0.092
0.119
0.159
I
4
0.077
0.087
0.098
0.109
0.107
0.123
0.138
O.IS3
0.139
0.158
0.178
0.198
0.186
0.213
0.239
0.266
0.120
0.131
0.169
0.184
0.218
0.238
0.292
0.319
0.142
0.200
0.257
0.34-5
0.153
0.21S
0.277
0.372
i|
0.164
0.230
0.297
0.399
2
0.175
0.246
0.317
0.425
arrangement of table in thousandths allows the nearest e\ inch to
be taken. The best plan is to take the allowance for the angle at i
inch depth as a constant and figure out the allowance for the partic-
ular depth wanted from the expression
CD
Draft allowance = •
Where C = a constant and D = the depth in inches.
Making Types
A type, shown in Fig. 2, is generally used as a guide for chipping
and scraping out the spherical end of the semicircular part E. It is
Mean Angle
of Drafc
Fig. 2
Fig. 3
not usual to make the curve on the end conform to any particular
mean angle of draft. Most diesinkers merely turn the end of the
type to a curve that looks right to the eye. However, uniformity
is desirable in these curves and Table 2 is given as a help in that
DROP FORGING DIES
463
Table 2. — Mean Draft of Spherical End of Cylindrical
Type
When Radius of End of Type is
Mean Angle of Draft in Degrees is
2^ X Diameter of Type
2i X " " "
2 X " " "
if X " " "
5i
74
,,90-V
Fig. 4
direction. It gives the values of the mean angle of draft with various
radii expressed in terms of the diameter of the type. It will be noted
that if the radius r is made twice the diameter of the type the mean
angle of draft is 7 J degrees. This rule is easy to remember and a
good one to adopt as standard. A good and easy way to get a close
approximation to the required curve is as follows: Turn a cylinder
of tool steel to the required diameter. Face the end square, scratch
off the distance G H equal to the allowance for draft obtamed from
Table i, remembering that the depth is half
the diameter of the t^-pe. Turn the end to a
curve which is uniform to the eye from the
center to the scratched line H. After the type
is hardened it is ready for use.
Semicircular impressions are finished with
ball cutters of the correct diameter. When a
ball cutter of the correct diameter is not at
hand and the job will not warrant making one,
the following method may be used. The center
line of the impression is projected to the end of the die. A semicircle
is scribed on the vertical surface of the end. After the impression is
roughed out, a smaller ball cutter is placed in the chuck of a diesink-
ing machine and the knee and slides manipulated until the cutter is
in proper relation to the semicircle as shown in Fig. 3. A square is
used to indicate when the curves of cutter and semicircle are coinci-
dent, as at /. The micrometer dials are now set, the lateral slide
locked, the knee lowered, the longitudinal slide operated until the
cutter is in position over the impression and the ball tool sunk into
the die until the micrometer comes to the position set at the semi-
circle on the end. A longitudinal cut is taken with this setting. The
cutter is then placed in another lateral position and the operation of
setting and cutting repeated. It may be necessary to perform this
operation several tim.es, and even then the result will be a series of
gutters and ridges instead of a uniform, sernicircular depression.
This can be readily corrected with the scraper and riffler.
< An aid in testing the accuracy of semicircular impressions is shown
in Fig. 4. If the semicircle is true, the corners of the square will
touch in all positions when the sides are resting on the edges of the
impression. If the square rocks on the corner in any position, that
spot is high and must be scraped down. This test must be made
before the "flash" is milled in the die.
464 HANDLING WORK
KNOTS AND SLINGS FOR HANDLING WORK
The knots described have been useful in work in out-of-the-way
places. No. i indicates the meaning of the terms employed.
No. 2, Simple or Overhand Knot. — The simplest of all knots to tie,
and may be used as a stop on a rope. A free end is necessary to
make it. If strained, it injures the fiber of the rope more than a
figure-8 knot, and it is difficult to unmake and liable to jam.
No. 3, Double Overhand Knot. — Used for the end of a rope when
it is required to prevent its going through an eye, as in a pulley block
or for the end of a halter rope. Also useful for shortening a rope and
may be made with any number of turns : A in the illustration shows
the first position; B, the knot finished with two turns; and C, one
with four full turns of rope.
No. 4, Figure-S Knot {Flemish). — May be employed as a stop on a
rope; is less injurious to the fiber of the rope, and more easily undone
than either the single or double overhand knot. If made with the
rope doubled and the bight left long, it becomes a figure-8 hoop
knot.
No. 5, Stevedore Knot. — End of the rope is wrapped twice around
the standing and then passed through the eye. Useful as a stop on a
rope to prevent the end going through an eye, as in a pulley block
(see double overhand knot). Also employed instead of sewing the
rope end with twine.
No. 6, Boat Knot {Marline-spike Hitch). — Suitable for quickly
making a rope ladder, or getting a temporary pull on a rope with a
marline-spike. No free ends required to form this knot. Point
marked A must always be at the back of the spike or rung of the
ladder, away from the direction of the weight or pull.
No. 7, Slip Knot {Simple Running Knot). — The simplest kind of
slip knot. It may be used similarly to the packer's knot, but is not
so good, as it is Hable to pull through and does not bind on the rope.
No. 8, Tomfool Knot {Double Running Knot). — When the loops
are drawn taut and the ends tied, this makes a pair of handcuffs
which it is almost impossible for the person so secured to undo. It
may be used as a barrel sling, half-hitches being put on the ends, and
the hook put under the knot itself. The bight marked 3 is passed
through the overhand loop as shown by the dotted line.
No. 9, Flemish Loop. — This knot makes a simple loop for light
work and may be used in the same way as a bowhne, but is not so
quickly made; neither is it so secure nor so easily undone. The
security depends almost entirely upon the check knot.
No. 10, Bowline. — A generally useful knot when a loop of any
sort that will not slip is required, as in a sling for lowering a man, or
fastening a bucket to a rope.
No. II, Bowline II. — A method of attaching the end of one rope
to the standing of another. A half turn is put in the standing and the
USEFUL KNOTS
46S
end of the other rope taken through as if tying an ordinary bowline.
This knot is practically a sheet bend.
(20)
'a / -rt ' B '"^ Fi&herman'&
Z c''"„H^h 5furK,ail Halyard Bend Bend Larks Head
51aCkWaII Hitch /;»•> M^^ppi^H F!chArrr,/,n'<.
(i&) Modified Fisherman's
Bends
iVo. 12, Running Bowline. — As shown in the first position a half
turn is made at A (sho\vn dotted) and the end is passed through and
to the back of the part marked B. This is a good slip knot and does
not tighten on the standing, always remaining open.
466 HANDLING WORK
No. 13, Bowline on a Bight. — The part marked A is passed behind
B and then in the direction of the arrow to C. The bight B is then
pulled taut. The two loops of this knot may be used as a man sling,
a barrel sling, or as a double man-harness, one loop under each
shoulder. When tightened it will not slip.
In case of an injured man, one of the loops can be kept shorter
than the other and adjusted under the armpits, the man being
seated in the larger loop.
No. 14, Open-hand Loop Knot and Figure-S Loop Knot. — The
upper loop knot is the one in common use and is adapted principally
for small ropes. The lower, or Figure-8 knot, is a better form and
may be used on a larger rope as it injures the fiber less than the
common form. These knots require a greater length of rope than the
bowlines, but ma}^ be used in similar ways.
N'o. 15, Man-harness Knot. — This knot can be tied in a rope with
neither end free. The bight A is pulled through under B and over
C, and the knot pulled taut. It is useful as allowing a number of
men to get a good purchase on a rope for hauling; also to put loops
in the rope to receive hooks at points other than the ends. •
No. 16, Packer's Knot. — A modification of a simple slip knot, but
has the advantage, when pulled tight, of biting on the standing at
A and not easily slipping back. It is particularly useful for cording
up rolls of camp bedding, €tc. It can be made permanent by an
added half hitch on the standing.
No. 17, Blackwall Hitch. —:■ A convenient method for returning an
empty rope on a hook. With a greasy rope, method B holds better.
No. 18, Modified Fisherman's Bends. — These are given as alter-
natives for securing ropes to poles or bars, and are adapted to heavy
strains.
No. 19, Fisherman's Bend. — A better method than the gooseneck
or lark's head (Fig. 20) for securing a rope to a chain or link. It is
also used to fasten the rope to a bar or the bail of a bucket. Lashing
at yl is necessary to prevent pulling through. As shown in first
position, two turns are taken over the link and the end brought back
in front and passed through the turns as shown dotted.
No. 20, Lark's Head. — Useful for fastening a rope to the link of a
chain or to a ring in a wall or box. It is not a secure knot unless lashed
at ^ . B shows a toggle inserted to prevent sHpping. C is a modified
gooseneck on a bar, suitable for securing the end of a rope in scaffold-
ing. The end must be placed at the back and the whole pulled taut.
No. 21, Half Hitch. — A quick and simple way of securing a rope
to a timber when no great pull is expected. The rope end is placed
under the pole, then back over to the right as shown. The end must
always be placed right at the back away from the pull, as sho\ATi at A.
The right-hand sketch shows the hitch with a slip to facilitate undoing.
No. 22, Timber Hitch. — This is the best and simplest of all timber
hitches and may be used for towing or otherwise handling timber,
rods, pipes, etc.; also for starting lashings on scaffolding or any
kind of pole work. For raising or lowering timber, the half hitch
should be placed high above the center of gravity to avoid slanting.
USEFUL KNOTS
467
No. 23, Clove Hitch. — This is one of the most useful of all hitches,
as it will take a strain in either direction wdthout slackening. It is
used for mooring ships heads of derricks for guy lines and all kinds
of rigging work. It may be easily undone, or a bight may be put in
(2Z)-"nmber Hitch i ^^//
,,,(23) Clove Hitch
(24) Rolling Hitch
£6h 56
(21) Half mtch
^,.M^
(25) Sheet 5end in Eye, u
Generally Used forcin "*
Adjustable
^Slinq
(25) Square or
Reef-Knot used
onlyforjoining
Two Ropes Together
(27) Slinging A Plank
.On Ed^e for Scaffolding
(26) Sheep's Shcinkfor
Ta king-Up Slack
(2?) A Bowline in A &ight
(35) Studding Sail Hitch
Useful in Hoisti ng Timber
(50) Clove or Double Half-
Hitch
(52) Clove or Double
(5!) Timber H/tch ^^^il'n.ti''^^'^ ^^"^^ Timberand Half-
torNaulmg Hitch., Useful in Hoisting
Shafts; or Tim be rain
Vertical Positions
(35; The Right Waii to Rig q ToCkle
468 HANDLING WORK
instead of one end to use as a slip. When commencing to tie the hitch
on a horizontal bar, the rule is over and back below, or the reverse of
the procedure in tying a half hitch.
No. 24, Rolling Hitch. — This lashing is used for getting a grip on
a large rope with a smaller one. Made in a chain it can be applied
to wire ropes and will not slip when the load has been taken up.
It is also suitable for hauling on electric cables, or withdrawing
diamond driU or other rods. For securing the end A may be brought
down and be lashed to the large rope. In making, the end is passed
over the spar twice, thM returned back as shown at (3), then over
behind as at (4), and up and under as at (5).
No. 25. — A square or reef knot, used only for joining two ropes
together.
No. 26. — Sheet bend in an eye, generally used for an adjustable
sling.
In supporting a swinging scaffold, it is often advantageous to U3e
light material , while, at the same time, strength is required. A plank
on edge is a great deal stiffer than the same plank laid flat, and No.
27 shows how to sHng a plank edgewise b}'^ a rope so that it will stay.
The knot used is a very simple one. A clove hitch is made around the
end of the plank; then one of the parts is twisted around the plank,
until the ends lead as shown in the sketch.
Very often it is desirable to shorten a piece of rope without cutting
it. No. 28 shows a sheep's shank which is used for this purpose.
The rope is brought back on itself, making two or more bights, and
a half hitch is taken around each bight. This knot will not slip,
and will nearly fall apart of its own accord if the strain is released,
so that when there is a liability of this happening, it is well to pass
a piece of wood through the loop A at each end and pull the rope
tight on them.
One of the handiest knots to know is a bowline. The bowline will
not slip, and is easy to untie. It can also be tied in the bight of a
rope, and is then called a "bowline in a bight." The steps required
to tie it are shown at No. 29. It is particularly handy when it is
necessary to hitch an auxiliary tackle on a fall to get additional pur-
chase for a heavy lift. This knot has aU the good points of the
simple bowline.
In using a block and fall for pulling things, there is a right way
and a wrong way of doing it. No. 35 shows the right way, W being
the weight to be moved. If A were the weight and W the post, the
blocks being left as shown, then it would be wrong. The advantage
of the right way of doing it is that the leverage due to one additional
part of rope in the tackle is gained! thus a three-part fall, rigged in
the right way, is as good as a four-part fall rigged in the wrong way,
and has the additional advantage that there is one less sheave with
its friction. In hfting a heavy weight, it is sometimes desirable to
put a tackle on the fall to gain additional leverage; the common
practice in a case of this kind is to hitch the auxiliary tackle to a
*'dead man." The right way is to hitch this tackle to the piece to
be lifted alongside the main tackle, which adds considerably to the
SAFE LOADS FOR ROPES AND CHAINS
469
leverage, being equivalent to one more part to the main fall besides
the gain by the use of the auxiliary fall.
No. 30. — Clove or double half hitch.
No. 31. — Timber hitch.
No. 32. — Clove or double half hitch as used for hauHng.
^0. 2,2)- — Studding sail hitch as used in hoisting timber.
No. 34. — Timber and half hitch. Useful in hoisting shafting or
timber in a vertical position.
SAFE LOADS FOR EYE-BOLTS AND FOR ROPES
AND CHAINS
Table i. — Safe Loads for Eye-Bolts
A
Inches
B
C
Safe
Load, Lb.
i|
iH
1,100
1,500
1,800
2,800
Drop-forged steel
I
I
I 5
I f
2
It
IP,
31*6
31-8
it
1 1^6
3, goo
5,100
8,400
12,200
16,500
21,800
D.B G. iron E.L., 28,000 lb. per 1
If
3
4
10,000
1 1 ,000
sq. in., welded j
2
5
14,000
^
2\
6
16,000
Table 2. — Safe Loads on Ropes and Chains
Manila Rope, Safe Load
in Tons
Wire Cable, Safe Load
in Tons
Chains, Safe Load in Tons
^
■t
<- c
^
■K
^ c
ti
t:
0^
O-H
rt
«=^
c— 1
S
11
0
3
a
Ph
.11
(£
PL,
3
Cos;
cA;«
H
tJ
uu
^«
^
fx;
P'O
LnU
H
i^
i
*
,
I
2
3*
1
*
I4
I^
1
1
Ij
3*
6^
f
I
3
li
f
2-
42
9
§
2
3-
6
5
I
2
1
3i
6
12
f
3
5
9
li
2i
4
8
16
5
9
IS
If
I
2
3
6
12
24
6
loi
18
i^
li
2i
4
10
19
36
I
8
14
24
2
4
6
13
25
48
li
II
19
33
5
8
16
32
60
li
13
23
39
i
3-
"J
II
li
18
32
54
2^
4-
8
13
GENERAL REFERENCE TABLES
COMMON WEIGHTS AND MEASURES
Linear or Measure of Length
12 inches = i foot. 3 feet = i yard.
5§ yards = i rod. 40 rods = furlong.
8 furlongs = i mile.
Equivalent Measures
Inches Feet
Yards Rods Furlongs
36 = 3
198 = 16.5
7920 = 660
63,360 =5280
= 5-5 = I
= 220 == 40 = I
= 1760 = 320 = 8
Mile
Square Measure
144 square inches = i sq. foot. 30^ square yards =1 sq. rod.
9 square feet = i sq. yd. 160 square rods = i acre.
640 acres = i sq. mile.
Equivalent Measure
Sq. Mi. A. Sq. Rd. Sq. Yd. Sq. Ft. Sq. In.
I = 640 = 102,400 = 3,097,600 = 27,878,400 = 4,014,489,600
Cubic Measure
1728 cubic inches = i cubic foot. 128 cubic feet = i cord.
27 cubic feet = i cubic yard. 24I cubic feet = i perch.
I cu. yd. = 27 cu. ft. = 46,656 cu. in.
Weight — Avoirdupois
437.5 grains = i ounce. 100 pounds = i hundred weight.
16 ounces = i pound. 2000 pounds = i ton.
2240 pounds = 1 long ton.
I ton = 20 cwt. = 2000 lbs. = 32,000 oz. = 14,000,000 gr.
Weight = Troy
24 grains = i pennyweight. 20 pwt. = i ounce.
12 ounces = i pound.
I lb. = 12 oz, = 240 pwt. = 5760 gr.
470
WEIGHTS AND MEASURES 471
Dry Measure
2 pints = I quart. 8 quarts = i peck.
4 pecks = I bushel
I bu. = 4 pk. = 32 qt. = 64 pt.
U. S. bushel = 2150.42 cu. in. British = 2218.19 cu. in.
Liquid Measure
4 gills = I pint. 4 quarts = i gallon.
2 pints = I quart. 31 J gallons = i barrel.
2 barrels or 63 gals. = i hogshead.
I hhd. = 2 bbl. = 63 gals. = 252 qt. = 504 pt. = 2016 gi.
The U. S. gallon contains 231 cu. in. = .134 cu. ft.
One cubic foot = 7.481 gallons.
One cubic foot weighs 62.425 lbs. at 39.2 deg. Fahr.
One gallon weighs 8.345 lbs.
For rough calculations i cu. ft. is called yl gallons and i gallon
as 81 lbs.
Angles or Arcs
60 seconds = i minute. 90 degrees = i rt. angle or quadrant.
60 minutes = i degree. 360 degrees = i circle.
I circle = 360° = 21,600' = 1,296,000".
I minute of arc on the earth's surface is i nautical mile =1.15
times a land mile or 6080 feet.
Weight of a Cubic Foot of Substances
Average
Names of Substances Weight
Lbs.
Anthracite, solid, of Pennsylvania 93
" broken, loose 54
" " moderately shaken 58
" heaped bushel, loose (80)
Ash, American white, dry 38
Asphaltum 87
Brass (Copper and Zinc), cast 504
" rolled 524
Brick, best pressed 150
" common hard 125
" soft, inferior 100
Brickwork, pressed brick 140
" ordinary 112
Cement, hydraulic, ground, loose, American, Rosendale 56
Louisville 50
" " " " English, Portland 90
Cherry, dry 42
Chestnut, dry 41
Coal, bituminous, solid 84
" " broken, loose 49
bushel, loose (74J
472 GENERAL REFERENCE TABLES
Weight of a Cubic Foot of Substances — Continued
Average
Names of StrssTANCEs Weight
Lbs.
Coke, loose, of good coal 27
" " heaped bushel 38
Copper, cast 542
" rolled 548
Earth, common loam, dry, loose 76
" " " " moderately rammed 95
Ebony, dry 76
Elm, dry 35
Flint 162
Glass, common window 157
Gneiss, common 168
Gold, cast, pure, or 24 carat 1204
" pure, hammered 1217
Granite 170
Gravel, about the same as sand, which see.
Hemlock, dry 25
Hickory, dry 53
Hornblende, black 203
Ice 58.7
Iron, cast 450
" wTought, pure 485
" " average 480
Ivory 114
Lead 711
Lignum Vitae, dry ^2>
Lime, quick, ground, loose, or in small lumps 53
" "■ " " thoroughly shaken 75
Limestones and Marbles 168
'' " " loose, in irregular fragments 96
Mahogany, Spanish, dry 53
" Honduras, dry 35
Maple, dry 49
Marbles, see Limestones.
Masonry, of granite or limestone, well dressed 165
" " sandstone, well dressed 144
Mercury, at 32° Fahrenheit 849
Mica 183
Mortar, hardened 103
Mud, dry, close 80 to no
" wet, fluid, maximum 120
Oak, live, dry 59
" white, dry 52
" other kinds 32 to 45
Petroleum 55
Pine, white, dry 25
" yeUow, Northern 34
" " Southern 45
WEIGHTS AND MEASURES
473
Weight of a Cubic Foot of Substances — Continued
Average
Names of Substances Weight
Lbs.
Platinum 1342
Quartz, common, pure 165
Rosin 69
Salt, coarse, Syracuse, N. Y 45
" Liverpool, fine, for table use 49
Sand, of pure quartz, dry, loose 90 to 106
" well shaken 99 to 117
" perfectly wet 120 to 140
Sandstones, fit for building 151
Shales, red or black 162
Silver 655
Slate 175
Snow, freshly fallen 5 to 12
" moistened and compacted by rain 15 to 50
Spruce, dry 25
Steel 490
Sulphur 125
Sycamore, dry ^1
Tar 62
Tin, cast 459
Turf or Peat, dry, unpressed 20 to 30
Walnut, black, dry 38
Water, pure rain or distilled, at 60° Fahrenheit 62^
" sea 64
Wax, bees 60.5
Zinc or Spelter 437
Green timbers usually weigh from one-fifth to one-half more than dry.
WATER CONVERSION FACTORS
U. S. gallons X 8.33 = pounds.
U. S. gallons X 0.13368 = cubic feet.
U. S. gallons X 231 = cubic inches.
U. S. gallons X 0.83 = English gallons
U. S. gaUons X 3-78 = liters.
English gallons (Imperial) X 10 = pounds.
English gallons (Imperial) X 0.16 = cubic feet.
English gallons (Imperial) X 277.274 = cubic inches.
English gallons (Imperial) X 1.2 = U. S. gallons.
English gallons (Imperial) X 4'537 = liters.
Cubic inches of water (39-1°) X 0.036024 = pounds.
Cubic inches of water (39.1°) X 0.004329 = U. S. gallons.
Cubic inches of water (39-i°) X 0.003607 = English gallons.
Cubic inches of water (39.1°) X 0.576384 = ounces.
Cubic feet (of water) (39-1°) X 62.425 = pounds.
Cubic feet (of water) (39-1°) X 748 = U. S. gallons.
Cubic feet (of water) (39-1°) X 6.232 = English gallons.
Cubic feet (of water) (39.1°) X 0.028 = tons.
Pounds of water X 27.72 = cubic inches.
Pounds of water X 0.01602 = cubic feet.
Pounds of water X 0.12 = U, S. gallons.
Pquu^s of water X Q-iQ = English gallons,
474
GENERAL REFERENCE TABLES
CONVENIENT MULTIPLIERS
Inches
Inches
Inches
X 0.08333
X 0.02778
X 0.00001578
feet.
yards.
miles.
Sq. inches
Sq. inches
Cu. inches
Cu. inches
X 0.00695
X 0.0007716
X 0.00058
X 0.0000214
Sq. feet.
Sq. yards.
Cu. feet.
Cu. yards.
Feet
Feet
X 0.3334
X 0.00019
yards,
miles.
Sq. feet X
Sq. feet X
[44
0.1112
Sq. inches.
Sq. yards.
Yards X 36 = inches. Cu. feet X 1728 = Cu. inches.
Yards X 3 = feet. Cu. feet X 0.03704 = Cu. yards.
Yards X 0.0005681 = miles. Sq. yards X 1296 = Sq. inches.
Miles
Miles
Miles
X 63360
X 5280
X 1760
inches.
feet.
yards.
Sq. yards X 9
Cu. yards X 46656
Cu. yards X 27
Sq. feet.
Cu. inches.
Cu. feet.
Avoir, oz. X 0.0625 = pounds.
Avoir, oz. X 0.00003125 = tons.
Avoir, lbs. X 16 = ounces.
Avoir, lbs. X 0.0005 = tons.
Avoir, tons X 32000 = ounces.
Avoir, tons X 2000 = pounds.
THE METRIC SYSTEM
The Metric System is based on the Meter which was designed to be one ten-
millionth (igonocoo) part of the earth's meridian quadrant, through Dunkirk and
Formentera. Later investigations, however, have shown that the Meter exceeds one
ten-millionth part by almost one part in 6400. The value of the Meter, as authorized
by the U. S. Government, is 39.37 inches. The Metric system was legalized by the
U. S. Government in 1866.
The three principal units are the Meter, the unit of length, the liter, the unit of
capacity, and the gram, the unit of weight. Multiples of these are obtained by pre-
fixing the Greek words: deka (10), hekto (100), and kilo (1000). Divisions are
obtained by prefixing the Latin words: deci (^), centi (xha), and milli dg'in))- Abbre-
viations of the multiples begin with a capital letter, and of the di\isions wth a small
letter, as in the followmg tables:
Measures of Length
10 millimeters (mm)
10 centimeters
10 decimeters
10 meters
10 dekameters
ID hektometers
centimeter cm.
decimeter dm.
meter m.
dekameter Dm.
hektometer Hm..
kilometer Km.
Measures or Surface (not Land)
100 square millimeters (mm^) = i square centimeter cnA
100 square centimeters = i square decimeter dm^.
100 square decimeters = i square meter m^.
Measures of Volume
1000 cubic millimeters (mm^) = i cubic centimeter cm*.
1000 cubic centimeters = i cubic decimeter dm^.
1000 cubic decimeters * . . . = i cubic meter viA
CONVERSION TABLES
475
lo milliliters (ml)
lo centiliters ....
lo deciliters
lo liters
lo dekaliters
lo hektoliters
Measures of Capacity
I centiliter cl.
I deciliter dl.
I liter 1.
I dekaliter Dl.
I hektoliter HI.
kiloliter
.Kl.
NOTK. — The liter is equal to the volume occupied by i cubic decimeter.
lo milligrams (mg)
lo centigrams
lo grams
lo dekagrams .
lo hektograms.
looo kilograms
Measures of Weight
I centigram eg.
I decigram dg.
lo decigrams = i gram
dekagram Dg.
I hektogram Hg.
I kilogram Kg.
I ton T.
Note. — The gram is the weight of one cubic centimeter of pure distilled water
at a temperature of 39.2° F., the kilogram is the weight of i liter of water; the ton is
the weight of i cubic meter of water.
METRIC AND ENGLISH CONVERSION TABLE
f 39.37 inches.
-j 3.28083 feet.
[ 1.0936 yds.
Measures of Length
I meter
I centimeter = .3937 inch.
I .03937 inch, or
I millimeter = \ £_
I 25 inch nearly.
I kilometer = 0.62137 mile.
I foot = .3048 meter.
I inch = ( 2.54 centimeters.
( 25.4 millimeters.
( 10.764 square feet.
I square meter = | ^.i^g square yds.
I square centimeter = .155 sq. in.
I square miUimeter = .00155 sq. in.
Measures of Surface
I square yard = .836 square meter.
I square foot.= .0929 square metei
.0929 square meter.
<,^„„„ in - i ^•452 sq. centimeters:
square m. - \ ^^^^ ^^_ millimeters.
Measures of Volume and Capacity
r 35-314 cubic feet.
I cubic meter = ■! 1.308 cubic yards. <
1.264.2 gallons (231
cubic inch).
, cubic decta«er=|^'-^™biy-
I cubic centimeter = .061 cubic inch.
I cubic decimeter.
61.023 cubic inches.
.0353 cubic foot.
1.0567 quarts (U. S.)
.2642 gallons (U. S.)
2.202 lbs. of water at 62° F.
I liter
I cubic yard = .7645 cubic meter.
r .02832 cubic meter.
I cubic ft. = ■! 28.317 cubic decimeters.
[ 2S.317 liters.
I cubic inch = 16.387 cubic centimeters.
I gallon (British) = 4.543 liters.
I galloH (U. S.) = 3.785 liters.
Measures of Weight
I gram = 15-432 grams.
I kilogram = 2.2046 pounds.
' ,9842 ton of 2240 lbs.
I metric ton = ^ 19.68 cwts.
2204.6 lbs.
I grain = .0648 grams.
I ounce a^voirdupois = 28.35 grams.
I pound = .4536 kilograms.
f^r, «f „,.« iKe J 1.016 metric tons.
I ton of 2240 lbs. = \ j^^6 kilograms.
476
GENERAL REFERENCE TABLES
Miscellaneous Conversion Factors
I kilogram per meter = .6720 pounds per foot.
I gram per square millimeter = 1.422 pounds per square inch.
I kilogram per square meter = 0.2084 pounds per square foot.
I kilogram per cubic meter = .0624 pounds per cubic foot.
I degree centigrade =1.8 degrees Fahrenheit.
I pound per foot = 1.488 kilograms per meter.
I pound per square foot = 4.882 kilograms per square meter.
I pound per cubic foot = 16.02 kilograms per cubic meter.
I degree Fahrenheit = .S556 degrees centigrade.
I Calorie (French Thermal Unit) = 3.968 B. T. U. (British Thermal Unit).
1 Horse Power = j ^3^°°^°/j^; P°"^ds per minute.
I Watt (Unit of Electrical Power) = \ /"^'^^fS*?'"^ ^T^'"- • ,
^ ' ( 44.24 toot pounds per minute
f 1000 Watts.
I Kilowatt = -j 1 .34 Horse Power.
[ 44240 foot pounds per minute.
Decimal Equivalents of Fractions of Millimeters,
v.^ncing by 1^0 mm-)
(Ad-
mm.
Inches
mm.
Inches
mm.
Inches
mm.
Inches
Th =
.00039
t¥^ =
.01024
TVd =
.02008
# =
.02992
ih =
.00079
# =
.01063
jVs =
.02047
t'oV —
.03032
t!(J =
.00118
T oV —
.01102
t¥o =
.02087
# =
.03071
ih =
.00157
tVo =
.01142
t¥o =
.02126
tVo -
.03110
T§?r =
.00197
T%% =
.01181
t¥o =
.02165
1^^^ =
•03150
ih =
.00236
.01220
/o% =
.02205
tVo =
.03189
tIo =
.00276
# =
.01260
tVo =
.02244
# =
.03228
T07 =
•00315
# =
.01299
tV7 =
.02283
tVo =
.03268
JOS =
•00354
tVo =
•01339
tVV =
.02323
T%% =
•03307
l's% =
.00394
t¥o =
.01378
t¥o =
.02362
tV% =
•03346
tVV =
.00433
T%% =
.01417
.02402
J%% =
•03386
TWU ~
.00472
^V =
.01457
J%\ =
.02441
T o'o =
•03425
tVo =
.00512
# =
.01496
T%\-
.02480
tVo =
•03465
# =
•00551
# =
•01535
i¥o =
.02520
T 0% =
•03504
t¥o =
.00591
1% =
.01575
tVo =
•02559
tVo =
•03543
tV(T =
.00630
tVo =
.01614
tVf =
.02598
jfo-
.03583
iVV =
.00669
tVo =
•01654
tVo =
.02638
"iVo —
.03622
.00709
tV7 =
.01693
tVo =
.02677
t¥o =
.03661
tV^ =
.00748
tVo =
.01732
tVo =
.02717
tVo =
.03701
T%% =
.00787
tVo =
.01772
t¥o =
.02756
tVo =
.03740
tVtt =
.00827
tVo =
.01811
ToV =
.02795
T%% =
.03780
^o\ =
.00866
TVd =
.01850
t¥o =
.02835
T% =
.03819
fo =
.00906
T^A =
.01890
tVo ~
.02874
t¥o =
.03858 ■
t¥(7 —
•00945
.01929
i'A =
.02913
t¥o =
.03898
^S% =
.00984
.01969
t¥o =
•02953
•03937
DECIMAL EQUIVALENTS OF MILLIMETERS 477
Decimal Equivalents of Millimeters and Fractions of Mil-
limeters. (Advancing by 5^0 mm. and i mm.)
mm.
Inches
mm.
Inches
mm. Inches
nim. Inches
M =
•03150
31 = 1.22047
71 = 2.79527
^^ =
.00079
to =
.03228
32 = 1.25984
72 = 2.83464
5^0 =
.00157
30 ~
•03307
33 = 1-29921
73 = 2.87401
* =
.00236
u- =
.03386
34 = 1-33858
74 = 2.91338
A =
•00315
u-
•03465
35 = 1-37795
75 = 2.95275
^^0 -
.00394
11 =
•03543
36 = 1.41732
76 = 2.99212
^> =
.00472
ft =
.03622
37 = 1-45669
77 = 3^03i49
^0- =
•00551
u-
•03701
38 = 1.49606
78 = 3.07086
A =
.00630
n =
.03780
39 = 1-53543
79 = 3-11023
x\ =
.00709
u =
.03858
40 = 1.57480
80 = 3.14960
M =
.00787
I =
•03937
41 = 1.61417
81 = 3.18897
H =
.00866
2 =
.07874
42 = 1-65354
82 = 3.22834
U-
•00945
3 =
.I1811
43 = 1. 6929 1
83 = 3-26771
lo =
.01024
4 =
.15748
44 = 1-73228
84 = 3-30708
u =
.01102
5 =
.19685
45 = 1^77165
85 = 3-34645
15. _
.01181
6 =
.23622
46 = 1.81102
86 = 3-38582
30 =
.01260
7 =
•27559
47 = 1-85039
87 = 3.42519
H =
•01339
8 =
.31496
48 = 1.88976
88 = 3.46456
io =
.01417
9 =
•35433
49 = 1-92913
89 = 3-50393
M =
.01496
10 =
•39370
50 = 1.96850
90 ^ 3-54330
lt =
•01575
II =
•43307
51 = 2.0078.7
91 = 3.58267
K- =
.01654
12 =
.47244
52 = 2.04724
92 = 3.62204
lo =
.01732
13 =
.51181
53 = 2.08661
93 = 3.66141
If =
.01811
14 =
•55118
54 = 2.12598
94 = 3-70078
M =
.01890
15 =
•59055 '
55 = 2.16535
95 = 3-74015
M =
.01969
16 =
.62992
.06929
56 = 2.20472
96 = 3-77952
If =
.02047
17 =
57 = 2.24409
97 = 3.81889
IJ =
.02126
18 =
.70S66
58 = 2.28346
98 = 3.85826
If =
.02205
19 =
.74803
59 = 2.32283
99 = 3.89763
U =
.02283
20 ==
.78740
60 = 2.36220
100 = 3.93700
U =
.02362
21 =
.82677
61 = 2.40157
a =
.02441
22 =
.86614
62 = 2.44094
c ^ - -
f 0 ~
.02520
23 =
•90551
63 = 2.48031
t^
u =
.02598
24 =
.94488
64 = 2.51968
0 <^ *^
u =
.02677
25 =
.98425
65 = 2.55905
fo ON ro t^
0 rO On <7
u =
.02756
26 = ]
.02362
66 = 2.59842
0 d r^ On
If =
•02835
27 = 1
.06299
67 = 2.63779
II II II II
to" =
•02913
28 = I
.10236
68 = 2.67716
iUi
fl =
.02992
29 = I
•14173
69 = 2.71653
if =
.03071
30 = I
.18110
70 = 2.75590
M IH H H,
478
GENERAL REFERENCE TABLES
Houi
O H w ro •'^ u-iO t-»00 a\ O M C) <^ "* too t^oO On O M N f^
HH
00 CM vq q ^00 cj ^ q 'f co <n o q rj-oq cs o q ^cq cj ^ q
fOOs-^6 io6\d M t^(N t^ rOCO "=i-Os'^6 vomO m r^OOO
iH M M M cs C4 <N N ror^rorO'^'^'^t'^uoiOiO loO
^+»
(N \q q ^00 f^ o q ^toq « o q 'f cx) <n o q -^oq <n o o^^t
W !>. rOOO fOC\46 lodo w t^<N J>- rOCO 4 On 4 O lO i-To
IH M M CM CM CM CM rofOfOro^^'^'^ioiOLo LoO
^
o o -"^co CM o q ■^cq cm o q •*oq <n o q "^oo cm o q 'tcq
6 \6 M vd CM* r^ rocd ro On 4 d lO d O M r^ N r^ rOGC 4 C\ 4
CI -^t^ONCM Ttt-ONC-i -^t^O CN lOt^O 0) uoi>.0 CM Lor^Q
M M H M 01 CM (N cocorOrOrfTj-'^TtLotouo loO
nw
M Tt-oq CM j>.H i^ONfor^M ^00 CM \q q ^j-cq (n >o q ^toq cm
CN^dsi^do mO cm" r^ rood rOON-^d lodvd M t^CM* t^ro
M ^O OnCM Tj-t^ONCN Tt-t^CN<M '^t-^O CM uot^O CM tot^O
M H M M CM CM CM (N rOCOfO'^'^^'st-LOLOlO VOMD
:i2
voCNc^J>-M ^CJnC^J^i-^ »J^<>c^t^iH i^ONCOr^M iJ^CscOl^
r^cM'od roc>4<>io dvD Mvd CM t^ coco CO (> 4 d lo d o h
H 'TO OnW 'to as<N ^l>-ON<N Ttt-.ONO) ^X^O M lOl^O
M M M M 0) <N CM CJ fOrOrOcO^xt-'^iOLOio mO
-
CNrOr^t-i i-OC^, roi>-M voO^cot^t-i iOGsfO'>'i-' i-OONfOr^i-i
iomO ci «>.cM'od fr)c>4oiooo Mvo CM t^ coco po o\ ■'t o
ti rfO C^M -^O QsM TtO ONCM ri-r^CAC^l Tj-f— OsCM Tfl^O
H M M w 0) CM M CM corOrOfO'*Tt-':t':J-Lovo LoO
<"IS
rot^M lioONCOr^M ^qN<^t^M •^q^'^f^"'^ '^^0^'^^'^ ^
46Niod lOMvd CM l>.0)od fOC^'tOsVoOO mO (N t^ rOOO
h-i roO C\ n -^O O 1-1 'to On m 'tO 0<N T^r^OsCM 'l-f^ON
M M M M CM (N CM CM COCOCOrO't't't'tLOLOlOlO
h!«
1>.M U->CNf01>-H ^ONfOf^M ^C>'^^'^ ^'?^^^'^ ^9^
CM od <^od 4c>i^d ir^Mvd CM t^cMGO codN'tONiooo mo
M roo 00 *-! cr;0 O i-< 'to On h 'tO On m rtO On cm rt r^ O^
M M M M CM 0) CM CM fOCOCOCO't't't'tlOU-iVOlO
^5
M voOnC01>.h lOOsfOt^H 'C'R^'^'^'^ ^9^*^*7"'^ ^'^^
M o M t^ CM 00 f^od 4oNiA)d lAiMvd c^ i>.cMod codN4c>vo
M roo 00 w roo 00 w roO On m 'tO On m 'rj-O On m 'tO On
M M M M o CM CM CM corororo't^'t'tvoiotou-)
nw
upovrpt^-iH loONfOi^M ^qNroi>.M loCNfot^M ^oq^fotT.
CN4d voMvd M r^cMcd rood 4cNiod iomo cm i^cmco co
coo 00 M coo 00 M roo CO w roO On w 't O On m ^O On
M (H M M 0) (N CM CM rOCOCOCO't'^t't'tVOlOlOLO
■-H
ONfot^-M i^iCNfor^-M i<^qNcor;-H ^qN^ot^M ^q^f^^T-i-J
r^ rood 4dN4d iomo w i>.c^cd rood 4dNiod i^mno cn
CO LOCO 0 roo 00 M r^yO 00 m roO CO m roO On « 'tO On
M H H M CM <M CN) 0) rOfOfOCO't't'st-^lOlOtOLO
r^-*
Tj- t^ M XT; q 'too 01 NO q 'ti>.'^ ^<?^'T^'\"'^ K^Q^'^'^^ ^
o H t^ oi od <^.co* 4 c> to d to w NO w t^ (N CO rocd 4 (> to d
CO tooO O CO tooO O COO CO M roo CO m roO CO H roO On
H H M M CM 01 01 01 rororoco't't-t'ttotototo
"S
oq CM NO q 'tpq cm no q 'toq <n o q 'toq <n no q 'toq cm no q
4d t^HNOH t^oiod rood 4 C^N to d t^ m no N J>. o< go' ro on
CO toco O ro tooO O ro toOO O roO CO m roO CO m roO CO
i_i M M M CM CM CM 01 rororOfO'^^^'ttotototo
Hoc
oiNO q 'toq NNO q ^toq ojno q -tco cm no q rj-oq nno q 't
rood 4dN4o tAjMvd m t^olod rood 4dNtod t^wNO oi j>.
01 to t^ O ro tooO O ro tooO O ro tocO O roO 00 m roO 00
M M M M 01 ci 01 01 corororo't't't'ttotnioio
^
NO q -toq 0) NO q ^toq cm o q -toq n o q rtoq <n o q "toq
H t^ oi t^ rood 4cN4d tA)MNd M r^oiod rood 4 ON to d t^
01 tot^O <N tot--0 ro tO;00 O ro toOO O ro toCO O roO 00
M IH M M CM Ol 01 CM rorororo't't'^'ttototoio
O
q '^oq CM o q 'toq <n o q 'tx '^^ o q "tco c^ o q -toq oj
dtodNOMt^oir^ rood 4d\4d toMNO m t^oiod rooo 't
Ol tot^O 01 tot^O 01 t^it^O ro toco O ro tooO O ro toQO
M M H M CM CM 01 01 fOrOrorO't't't'ttototOLO
^oul
O M 01 CO 't too t^OO On O M 01 ro rr too t^OO On O h Ol ro
DECIMAL EQUIVALENTS
479
Decimal Equivalents of Fractions of an Inch. (Advancing
BY StHS, i6tHS, 32NDS and 64THS.)
8ths
32nds
64ths
64ths
i = .250
i = -375
* = .500
I = -625
f = -750
i = .875
5 _
i6ths.
0625
18;.
3125
4375
5625
6875
if = -8125
if = -9375
A =
03125
A =■
09375
j,_ __
15625
/2 =
21875
/l =
28125
-B =
34375 •
M =
40625
33 —
46875
H =
53125
l^ =
59375
11 =
65625
71875
If =
78125
11 =
84375
If =
90625
M =
96875
6? = -015625
61 = -046875
6? = .078125
/f = .109375
^% = .140625
H = -171875
If = .203125
if = -234375
u
23
64
If
27
6¥
If
.265625
.296875
.328125
-359375
.390625
.421875
•453125
.484375
•515625
•546875
•578125
•609375
.640625
.671875
.703125
•734375
.765625
.796875
';28i25
•859375
.890625
.921875
•953125
•984375
Decimal Equivalents of Fractions of an Inch.
BY 64THS.)
(Advancing
6?
6?
S
H =
015625
H =
.265625
ff =
.515625
ff = .
.03125
^% =
.28125
H =
.53125
|!i:
.046875
H =
.296875
.546875
.0625
tV =
•3125
A =
.5625
if = .^
.078125
|i =
•328125
31 =
.578125
11 = -^
•09375
H =
.34375
|| =
.59375
M--i
.109375
M =
•359375
fl =
•609375
ff = .^
.125
i =
•375
i =
•625
i = .^
.140625
H =
.390625
U =
.640625
fl = ^^
.15625
M =
.40625
.65625
.171875
U-
.421875
64 =
.671875
If ^•c
.1875
T% =
•4375
ii =
.6875
if = ^c
.203125
II =
•453125
n =
•703125
li = .^
.21875
it =
•46875
M =
.71875
f i = •<^
.234375
f ¥ =
•484375
f^ =
.734375
f 4 = •<:
•25
i =
-50
i =
.75
765625
78125
796875
8125
828125
84375
859375
875
890625
90625
921875
9375
953125
96875
984375
48o GENERAL REFERENCE TABLES
Decimal Equivalents of Fractions below J^
Fractional Parts of an
[nch
Decimal
Decimal
Equivalents
Equivalents
6
7
8
12
14
16
24
28
32
64
,015625
I
•015625
.03125
I
2
•03125
.035714
I
•035714
.041667
I
.041667
.046875
3
•04687s
.0625
I
2
4
•0625
.071429
I
2
.071429
.078125
5
.078125
. .083333
I
2
•083333
.09375
3
6
•09375
.107143
3
.107143
.109375
7
•I0937S
.125
I
2
3
4
8
.125
.140625
9
.140625
.142857
I
2
4
.142857
.15625
5
10
•15625
.166666
I
2
4
.166666
.171875
II
.171875
.178571
5
.178571
.1875
3
6
12
•1875
.203125
13
.203125
.208333
5
.208333
.214286
3
6
.214286
.21875
7
14
.21875
•234375
15
•234375
•25
2
3
4
6
7
8
16
•25
.265625
17
•265625
.28125
9
18
.28125
.285714
2
4
8
.285714
.291666
7
.291666
.296875
19
•296875
•3125
5
10
20
•3125
.321429
9
.321429
.328125
21
•328125
.333333
3
4
8
•333333
•34375
II
22
•34375
•357143
5
10
•357143
•359375
23
•359375
•375
3
6
9
12
24
•375
.390625
25
.390625
.392857
II
•392857
•40625
13
26
.40625
.41666
5
10
.41666
.421875
27
.421875
•428571
3
6
12
.428571
•4375
7
14
28
.4375
•453125
29
.453125
•458333
II
.458333
.464286
13
.464286
.46875
15
30
.46875
•48437s
31
•48437s
•5
3
4
6
7
8 .
12
14
16
32
•5
DECIMAL EQUIVALENTS 48 1
Decimal Equivalents of Fractions between i" and 1"
Fractional Parts of an Inch
Decimal
Decimal
Equivalents
Equivalents
6
7
8
12
14
16
24
28
32
64
.515625
33
•51562s
•53125
17
34
.53125
•535714
15
•535714
.541666
13
.541666
•546875
35
•546875
•5625
9
18
36
.5625
•571429
4
8
16
.571429
•578125
37
.578125
•583333
7
14
•583333
•59375
19
38
•59375
.607143
17
.607143
•609375
39
.609375
.625
5
10
15
20
40
.625
.640625
41
.640625
.642867
9
18
.642867
.65625
21
42
•65625
.666666
4
8
16
.666666
.671875
43
•67187s
.678571
19
•678571
.6875
11
22
44
•6875
.703125
45
.703125
•708333
17
.708333
.714286
5
10
20
.714286
•71875
23
46
•7187s
■734375
47
•73437S
•75
6
9
12
18
21
24
48
•75
.765625
49
.765625
.78125
25
50
•78125
•785714
11
22
•785714
.791666
19
- .791666
.796875
51
•79687s
•8125
13
26
52
.8125
.821429
23
.821429
.828125
53
.828125
•833333
5
10
20
.833333
.84375
27
54
.84375
.857143
6
12
24
.857143
•859375
55
.859375
.875
7
14
21
28
56
.875
.890625
57
.890625
.892857
25
•892857
.90625
29
58
.90625
.916666
11
22
.916666
.921875
59
.921875
•928571
13
26
.928571
•9375
IS
30
60
•937S
•953125
61
.953125
•958333
23
•958333
.964286
27
.964286
•96875
3^
62
.96875
•984375
63
.984375
482
GENERAL REFERENCE TABLES
Decimal Equivalents of Fractions and Nearest Equivalent
64THS
Fr.
Decimal
Near-
est
64th
Fr.
Decimal
Near-
est
64th
Fr.
Decimal
Near-
est
64th
1
0.0313
0.0323
0.0333
0.0345
0.0357
0.0370
0.0385
0.0400
0.0417
0.0435
0.0455
0.0476
0.0500
0.0526
0.0556
0.0589
0.0625
0.0645
0.0667
0.0690
0.0714
0.0740
0.0769
0.0800
0.0833
0.0870
0.0909
0.0938
0.0952
0.0968
O.IOOO
0.1034
0.1053
0.I07I
O.IIII
O.II54
O.II76
0.1200
0.1250
0.1290
0.1304
i~.
2V
2^0
0.1364
0.1379
0.1429
O.1481
0.1500
0.1538
0.1563
0.1579
0.1600
O.1613
0.1667
0.1724
0.1739
0.1765
0.1785
O.1818
0.1852
0.1875
0.1905
0.1923
0.1935
0.2000
0.2069
0.2083
0.2105
0.2143
0.2174
0.2188
0.2222
0.2258
0.2273
0.2308
0.2333
0.2353
0.2381
0.2400
0.2414
0.2500
0.2580
\
1
2V
2«9
0.2593
0.2609
0.2632
0.2667
0.2692
0.2727
0.2759
0.2778
0.2800
0.2813
0.2857
0.2903
0.2917
0.2941
0.2963
0.3000
0.3043
0.3077
0.3103
0.3125
0.3158
0.3182
0.3200
0.3214
0.3226
0^3333
0.3438
0.3448
0.3462
0.3478
0.3500
0.3529
0.3548
0.3571
0.3600
0.3636
0.3667
0.3684
0.3704
0.3750
^\
il
2V
e\
1
1%
I
1
t\
2^
7
i
t
TO
tV
I
iV
if
i
t\
1
^\
X
1
tV
1
If
i
if
^%
h
u
i
/^
M
i
S
i
ti
tV
tV
4
1
^\
e\
i
1^
if
If
i
TT
i
its
A
i
DECIMAL EQUIVALENTS
483
Decimal Equivalents of Fractions and Nearest Equivalent
64THS
Fr.
Decimal
Near-
est
64th
Ft.
Decimal
Near-
est
64th
Fr.
Decimal
Near-
est
64th
H
A
0.3793
0.3810
0.3846
0.3871
0.3889
0.3913
0.3929
0.4000
0.4063
0.4074
0.4091
O.4118
0.4138
0.4167
0.4194
O.4211
0.4231
0.4286
0.4333
0.4348
0.4375
0.4400
0.4444
0.4483
0.4500
0.4516
0.4545
0.4583
0.4615
0.4642
0.4667
0.4688
0.4706
0.4737
0,4762
0.4783
0.4800
0.4815
0.4828
0.4839
0.5000
f
2I
if
ft
i
O.5161
0.5172
0.5185
0.5200
0.5217
0.5238
0.5263
0.5294
0.5313
0.5333
0.5357
0.5385
0.5417
0.5455
0.5484
0.5500
0.5517
0.5556
0.5600
0.5625
0.5652
0.5667
0.5714
0.5769
0.5789
0.5806
0.5833
0.5862
0.5882
0.5909
0.5926
0.5938
0.6000
0.6071
0.6087
O.6111
0.6129
0.6154
0.6190
0.6207
0.6250
33
6?
if
0.6296
0.6316
0.6333
0.6364
0.6400
0.6429
0.6452
0.6471
0.6500
0.6522
0.6538
0.6552
0.6563
0.6667
0.6774
0.6786
0.6800
0.6818
0.6842
0.6875
0.6897
0.6923
0.6957
0.7000
0.7037
0.7059
0.7083
0.7097
0.7143
0.7188
0.7200
0.7222
0.7241
0.7273
0.7308
0.7333
0.7368
0.7391
0.7407
0.7419
0.7500
f
tV
If
!t
ft
n
#
if
V^
V
tV
if
ii
5
i
IV
If
12
H
H
1
ft
p
tl
n
7%
f
A
1}
tV
H
A
i
10
If
8
M
7
To
if
i
If
«
t
fi
1
II
It
M
if
If
tl
if
f
tV
f
n
tV
if
^
If
if
fi
fi
il
i
ii
i
i
f
484
GENERAL REFERENCE TABLES
Decimal Equivalents of Fractions and Nearest Equivalent
64THS
Fr.
Decimal
0.7586
0.7600
0.7619
0.7647
0.7667
0.7692
0.7727
0.7742
0.7778
0.7813
0.7826
0.7857
0.7895
0.7917
0.7931
0.8000
0.8065
0.8077
0.8095
0.8125
0.8148
0.8182
0.8214
0.8235
0.8261
0.8276
0.8334
Near-
est
64th
H
Fr.
16
T9
27
20
23
27
41
13
T5
ft
27
3 1
22
25
if
23
ft
26
3T
19
2T
29
32
if
Decimal
0.8387
0.8400
0.8421
0.8438
0.8462
0.8500
0.8519
0.8571
0.8621
0.8636
0.8667
0.8696
0.8710
0.8750
0.8800
0.8824
0.8846
0.8889
0.8929
0.8947
0.8966
0.9000
0.9032
0.9048
0.9063
0.9091
0.9130
Near-
Near-
est
Fr.
Decimal
est
64th
64th
H
0.9167
U
0.9200
H
0.9231
M
n
It
0.9259
f!
0.9286
0.9310
0.9333
If
fi
0.9355
0.9375
0.9412
0.9444
0.9474
H
if
4f
0.9500
'i
If
0.9524
ft
U
0.9545
U
0.9565
U
0.9583
fi
If
0.9600
0.9615
0.9630
fi-
0.9643
ll
0.9655
ff
0.9667
It
0.9678
ti
H
0.9688
I.OOOO
M
!l
PRIME NUMBER FRACTIONS
485
TABLE OF PRIME-NUMBER FRACTIONS
The table shows decimal equivalents of common fractions having
prime numbers for both numerator and denominator. As an example,
suppose it is required to find the thread angle of a worm.
_ number threads
^ diametral pitch X pitch diameter
Find the angle of a worm 7 diametral pitch, 5 threads, 2-inch
P. diameter: Tangent angle = f X ^
Then from table
, , 0.7143
f = 0.7143 and — - — = 0.35715
which is the tangent for 19 degrees 21 minutes, nearly.
Prime Number Fractions and their Decimal Equivalents
Denominators (Prime Numbers Only)
I
97
89
83
79
73
71
67
61
59
53
47
43
.0103 .0112
.0120
.0126
•0137
.0141
.0149
.0164
.0169
.0189
.0213
•0233
■S
.0309 .0337
.0361
.0380
.0411
.0423
.0448
.0492
.0508
.0566
.0638
.0608
s
.0515 -0562
.0602
.ob33
.0685
.0704
.0746
.0820
.0847
■ 0943
.1064
.1163
7
.0722 .07S7
.0843
.0886
.0059' -0986
.1045
.1148
.1186
.1321
.1489
.1628
>>
II
.1134 .1236
.1325
.1392
.1507 .1549
.1642
.1803
.1864
• 2075
.2340
•2558
's
13
.1340 .1461
.15&6
.1646
.1781 .1831
.1940
■ 2131
.2203
•2453
.2766
•3023
1
17
.1753 -iQio
.2048
.2152
.23291 .2394
•2537
.2787
.2881
.3208
.3617
•3953
19
.1950 .2135
.2289
.2405
.2603
.2676
.283b
•3115
•3220
.3585
•4043
•4419
e
3
23
.2371 -2584
.2771
.2911
• 3151
•3299
•3433
•3770
.3808
• 4340
.4894
•5349
20
.2990 .3258
■3494
.3671
•3973
.4085
.4328
•4754
•4915
•5472
.6170
•6744
15
.^I
.3196 .3483
•3735
•3924
•4247
.4366
.4627
.5082
•5254
.S849
.6^06
.7209
•r'
37
.3814 -4157
•4458
.4084
.5068
.5211
•5522
.6066
.6271
.6981
.7872
.8605
41
.4227 .4607
.4940
• 5190
• 5615
• 5775
.6119
.b72i
.6949
• 77^6
■8723
•9535
^
43
•4433 -4831
.5181
•5443
.5890
.6056
.6418
.7049
.7288
.8113
.9149
'"'
47
.4845 -5281
.50b3
.5949
.0438
.6620
•7015
•7705
.7966
.8868
g
S3
.5464 .5955
.6380
.6709
.7260
•7465
.7910
.8689
.898s
d
SQ
.6082 .6629
.7108
.74O8
.8082
.8310
.8806
.9672
u
61
.6289 .6854
7349
.7722
.8350
.8592
.9104
67
.6907 .7528
.8072
.8481
.9178
•9437
^
71
.7320 7978
.8554
.8087
.9726
73
.7526 .8202
.8795
.9241
7Q
.8144 .8876
.9518
83
•8557-9326
89
•9175I
Denominators (Prime Numbers Only)
41
37
31
29
23
I
.0244
.0270
.0323
•0345
•0435
V
3
.0732
.0811
.0968
.IOJ4
.1304
M^
5
.1220
•1351
.1613
.1724
•2174
n"^
7
.1707
.1892
.2258
.2414
•3043
0
II
.26ii3
•2973
.3^58
•3793
.4783
(^ y.
13
•3171
■.?5i4
.4194
•4483
•5652
^-
17
.4146
•4595
.5484
.?862
•7391
^s
19
.4634
•5135
.6129
•6552
.8261
1^
23
.5610
.6212
.7419
•7931
29
• 7073
•7838
•9J55
31
.7561
•8778
37
.9024
19
.0526
•1579
.2632
.3684
•5789
.6842
•8947
17
13
"
7
5
.2000
.0588
.0769
.0909
.142.9
•1765
•2308
.2727
.4286
.6000
•2941
.3846
•4545
•7143
.4118
.5385
•6364
.6471
.8462
•7647
Only those common fractions having prime
numbers for both the numerator and denom-
inator are given in table. Others can be found
by simple multiplication or division.
486
GENERAL REFERENCE TABLES
Equivalents of Inches and Fractions of Inches in Decimals
OF A Foot
In.
o In.
I In.
2 In.
3 In.
4 In.
5 In.
.0833
.1667
.2500
'3333
.4167
■,\
.0026
•°!§9
.1693
.2526
•3359
•4193
¥
.0052
.0885
.1719
•2552
•3385
.4219
3%
.0078
.0911
.1745
.2578
•341 1
•4245
I
.0104
.0938
.1771
.2604
•3438
.4271
/l
.0130
.0964
.1797
.2630
.3464
.4297
A
.0156
.0990
.1823
.26s6
•3490
•4323
^
.0182
.1016
.1849
.2682
•3516
.4349
i
.0208
.1042
.1875
.2708
•3542
•4375
.0234
.1068
.1901
•2734
.3568
.4401
i
.0260
.1094
.1927
.2760
.3594
.4427
.0286
.1120
•1953
.2786
.3620
•4453
f
.0313
.1146
.1979
.2813
.3646
.4479
M
•0339
.1172
.2005
.2839
.3672
•4505
•0365
.1198
.2031
.2865
.3698
•4531
M
.0391
.1224
.2057
.2891
•3724
•4557
h
.0417
•1253
.2083
.2917
•3750
•4583
U
•0443
.1276
.2091
.2943
•3776
.4609
1^6
.0469
.1302
•2135
.2969
.3802
•463s
il
.0495
.1328
.2161
•2995
.3828
.4661
t
.0521
•1354
.2188
.3021
.3854
.4688
■ 2
•0547
.1380
.2214
•3047 .
.3880
.4714
■ '5
•0573
.1406
.2240
•3073
.3906
.4740
■ f
•0599
.1432
.2266
•3099
•3932
.4766
f
.0625
.1458
.2292
•3125
.3958
.4792
1*
.0651
.1484
.2318
•3151
.3984
.4818
if
.0677
.1510
•2344
.3177
.4010
.4844
u
.0703
•1536
.2370
.3203
.4036
.4870
i
.0729
•1563
.2396
.3229
.4063
.4896
•075s
.1589
.2422
•3255
.4089
.4922
1
.0781
.1615
.2448
.3281
•4115
.4948
.0807
.1641
.2474
•3307
.4141
•4974
EQUIVALENTS
OF DECIMALS OF A FOOT 487
Equivalents
OF Inches
AND Fractions of Inches in
OF A Foot
Decimals
In.
6 In.
7 In.
8 In.
9 In.
10 In.
II In.
1
.5000
.5026
.5052
.5078
.5104
•5130
•5156
.5182
•5833
•5859
.5885
•59 1 1
.5938
•5964
•5990
.6016
.6667
•6693
.6719
•6745
.6771
.6797
.6823
.6849
.7500
.7526
•7552
.7578
•8333
.8359
.8385
.8411
.9167
.9193
.9219
.9245
.7604
.7630
.7656
.7682
.8438
.8464
.8490
.8516
.9271
•9297
•9323
•9349
1
.5208
.5234
.5260
.5286
.6042
.6068
.6094
.6120
.6875
.6901
.6927
•6953
.7708
•7734
.7760
.7786
.8542
.8568
.8594
.8620
•9375
.9401 »
•9427
•9453
1
.5313
•5339
•5365
•5391
'.6146
.6172
.6198
.6224
.6979
.7005
.7031
•7057
.7813
•7839
•7865
.7891
.8646
.8672
.8698
.8724
•9479
•950s
•9531
•9557
if
•5417
•5443
.5469
•5495
.6250
.6276
.6302
.6328
.7083
.7109
.7135
.7161
.7917
•7943
.7969
•7995
.8750
.8776
.8802
.8828
•9583
.9609
•9635
.9661
1
11
.5521
•5547
•5573
•5599
•6354
.6380
.6406
.6432
.7188
.7214
.7240
.7266
.8021
.8047
.8073
.8099
•8854
.8880
.8906
•8932
.9688
.9714
.9740
.9766
1
11
•5625
.5651
•5677 •
•5703
.6458
.6484
.6510
.6536
.7292
•7318
• ^7344
•7370
.8125
.81S1
•8177
,8203
•8958
.8984
.9010
.9036
.9792
.9818
.9844
.9870
II
if
•5729
.5755
.5781
.5807
.6563
.6589
.6615
.6641
•7396
.7422
•7448
.7474
.8229
•8255
.8281
.8307
.9063
.9089
•9115
.9141
.9896
.9922
.9948
•9974
1
488
GENERAL REFERENCE TABLES
O OCO to H to Oi w
O O. ^ ^ OnoO in m
OOOOOOOOO OvM to
O w totor^OvtN •*
q M -^Nooo q ^"^
ovdvdvdvovd d d
■^•'t'^-^'ttototO
to O to O NO
too 00 M lO
'to 00 w to.
O M O OOO tNO
to roo too "to
"N OiNO 't tN 1-1 O
o 00 " 't t- o tov
to t^ O <N -t r- Ov
to to to 1
■00 O w O OwO
Ov t^ OvO t-* 't
to Tt- to to to •*
rooO M tJ-OO to to
O tN Tt O M t-.00 tt
to t-^ O IN lOOO IN t^
H O Ov OOO t^ r^O
to r^co O c-i -^vo 00
O NO O too r^O
to O MOO M M N
IN 00 -to r^ to CO
CO CO M OO M VOOO
O O O IN M to coo
too O 00 O IN lOOO
O CNJOO 'tw t^coOv
M ■ttot--.qvq c) CO
vOnOnOnOnO t^rit-^
•t
O ^00 O w O OvNO
OtNOvlNOvMt^Ov
O too r^cOMcJOO
O o) tot^ O totooo
O M o< to too r-00
NONdNONdvooNONd
COM w ^OvO to CO
Or^ttOMMOOOv
■o t 't t too i-~ Ov
M ri- t- O coo Ov IN
O M IN r^ too t- Ov
OnO O too r^O to
tOlOMMOOMM
M lOOcOt~-0)CO ^
O O IN O Ov coo o
q w to 't to t-.oq q
odooooodododod dv
CO Ov -too M
d dv On dv dv
CO
O OvOO to M to Ov M
O Ov Tf Tt- OvOO <N M
O cooo cooo rf M OO
O OvoQOO t-t-i^NO
O O M IN CO 'ttOO
ONOvdvOvdNdvOvdv
CO CO H OvO M lOOO
OlOOvt>MOCOM
r^oo On O M o< CO ^
dvddddddd
dddddMMM
CO't^COM
O CO to <M Tt
If III
•^00 O IH O OvNO CO<50 M Tf-^'-O to
r^ O f^ OO r^ 't o c^ -t O M r^oo
cs to Ov coco coOv tocsOvt^iocciM
't^^t^tt't
OOO coo t^O to to Ov -tCO M
ioOmoOmmO OOO-'t't
(N CO "t to t^ O too O to O to M
O CO O r~- "t CM O^ 't M OnO •*
OMCJCNco-t-tto Or^ t^oO On
O OnOO tOMVoOvW POCOM OvnO m tooO
O-^-tOvOvcotNt^ OOOitNMto coo
O M CO tooO tNOO iomOcoO
O coo OvMOOco OOcoi
O CO t^ >
Ov CO t^ <N O
00 On Ov O O
toto-tMOOiNM Ot^iN too O 't w VOOO Ov OvO
IN i^ M -t too toco OioOcotoOOto c>)00cot-O
Ot^-t-tOMtSCOOV lOtOMMOOMM OlOOOv-t
00<~Jt0O00M. toov'tOtOMt^-t csO OnoO t^ r^co O O <>) lo f^ M
OOOOOOm MMCjCNcO't'tto Of^ 1^00 O O M IN -t too t~- Oi
OOOOOOO OOOOOOOO OOOOOmmm mmmmm
HO r-V
si{;jno|-X}xis oj suopDBj j; pappy
SQUARES Ol^ NUMBERS
489
t^ fO I^
0
(O <N
MOO
^Oi
toi^O t-vO to 00
0
CO too 0
r^MOO
COO Ov 0 M OOO t
0 <N0O
O\o
rf 0> 0 lO
VOMMOOW^^>0
OOO IN M
to t t^
OOvt-MOiNOvM
0
t
Ovio
0 O\00 t^ t-OO Ov 0
r}- t^ M 10
o> ^o>
Otstot^qcstot^
•too M
«OD0
i-i 10
a>5"
0 0
Ttr^M lOOtor--!
0
0 -t Oi CO
t^ C^O
.0 r^ 0
•*
r- 0>
w ^0 o\
H too 00 0 to 1000
0
CO to t^ 0
10 losd
\o ^ vd 0
t^ ti
t^ t^
06000600 do^doi
.§
^SS^
M M M
iNpic^c^cocOcoco
IOLO>0
10 >r-
10 10 >o 10
.OIOIOIOIOIOIOIO
-000
00000000
0
t^
^- -t
toOsO (NvOOO 0 M
000 to mO
0 M CO
CO M Ov to M toco ov
00 t^ M
0
•0
in' ir>
^ t^
1000
-0 C>0 OvOoOOOO
to
0 CO 10 M
ts 0> 0
Or-iNtoOvOv-t^
0
to
0 M
r^ CO
ctSo'm'pi w!)^io
CO q "P^f^ovM to
ct> to t- 0
too M
loOO c^oo tocoM
M- ^ 5^
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r-oo
0
t^oo Oi M
M CO to
vooo Ov M cs -to 00
O30 0
N
TtOOO
q IN
^0
t-- qv M ^0 CO q
(N to q> « ^ "? t^-
M M <N
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to to
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co^^^-^^tovo
to
to too 0 0 06 ri
t-:. t-l t^ r^o6o6o6o6
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ftt-trfttt
0
ro CS
woo
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to lOvO t^O to 0 'O
0
CO too 0
r)- MOO
COO 0. 0 M 0 00 -t
10 tS r^
0
trl
r^oo
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0 0
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-too t~- M
0 ^IN
0 t r-O Ov t- 0 r-
\o t^=o
0
^ t^
00 t00f->O-iT0
r-OMN
to Ov cooo to Ov to <N
ro 0 r-
00
^'h
OvO
TtM Olt-^IN 000
0
^ ?! 0;« 0 -t to
M OvoOO to to P< M
<N
>+
0. "
cs ^
000 Ci M coiO t-CO
q
<N •fo O-
qvM to
too 00 0 IN -to 00
ddd
d
d
d d
d M
M M
MMMiNciriciiN
CO
CO CO to to
CO ^ "t
44-ttOlOlOlOto
CI O) ro
ro CO ro ro ro to
to CO
cotocotococococo
CO
to to CO to
CO CO CO
cotocococototoco
g
to t^
M to
-t ^
COOO PtOOO 0 M
000 to MO
0, M CO
CO M Ov ti-/ M toco Ov
ro r-O
00
IN 0
^O)
10 CO
0 'to -to coo to
to
mS'SS
t^ 0> to
OINCSOOOvttOv
000
0
CM -^VO 0
c^ \0
0 10 0 0 IN OiO -t
0 M Ct,
tooo M too tooo to
roo 0
0
to r-
0 -t
0
MO MO
MO M
0 M t^ tN t^ tooo t
00- CT H
<N
<OVOOOO <3
to 100 00 a M p) ^
t-00 0 M
to ^0
t^ Ov q IN to tovooo
do d
d
d
0 0
0 0
H M
MHMMM'rilNtN
IN
c4 cs to to to CO CO
cocot-ttt-tt
M M (N
0(
01
t- ^0^^
g
to t^
MOO
^ 0
CO 100 t^O CO 0 0
0
to too 0
■t MOO
t^O Ov 0 M 0 00 t
0 <N00
\o
r^ <o ^ 0^ 0 >o
0 M MOO M M .0
to OOO <N M
10 -tc-
OOvt-MOviNOvM
^<N 0
OvOvO
VO t^
0 -too IN r-. to Ov to
Ovt^O to
^^-t
too 00 M CO t^ 0 to
P» fO •*
iniOOOO
0 0
Tf lOOOO Ol M 0) rf
0
t^ Ov M toiO t^ 0
M CO tooo 0 M to t^
qvo M
10
^ loooq
00
M <N CO -t >o t-;-oq q^
0
M C< rt too t~00
0 M p< CO too »~^oq
M H M
2
d
M M
M 2
O) to
tototototococoto
^-t^-t-t-t^^
lAtOtolOlOtololo
C) ro <N
—
t^
to l^
M to ^ ■*
cooo c<ooo 0 M
000 to mO
OV M to
CO M OvtO M tooo Ov
00 t^M
g
to
-M^t?>cO
0 OvO 0>0 00 000
0 t>) loco t^O mO
0 to to M
c-j 0> 0
Ot^tN coOvOvtt
c«
t^vOOO
r^co
CC to (N OCOO 0
to too f-OO 0 coo
0 0 M
0 :« \D 'd-
Ovr-iotoiN 0 Ovr-
0
^ to IN M
C>00 1^
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cs to "t too t-|-00 Ov
p)
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lOO
f^OO
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0 t^oq q^ q> q M
vdvdvd
^
0
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00 t^t^t^t^t^t^
I>.
t^ ri !>. r^ t>.o6 06
0606060606060606
t^ <~0 !>.
g
to <N
MOO
■* C3\
CO voo r^o CO 0 0
0
CO too 0
rhMOO
2?0 Ov 0 M 0 00 t
VO M ro
r^oo
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00 M MOO M 0
0 M CO UTt^ 0 "too
•tOv^tOv^O voO
00 r- t-.oq Ov Ov q
to TJ-OO t^ M
0 ^M
0 t t^O Ovt^ Ov r^
t^
^ N
M 0
0 0
t^ MOO to
0) Ovr-
tott^tocottot^
w ^0
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0
M t^ INOO
Tj-Ovto
M t^toOvtOM r^co
M
CO to
^ ■*
lO 10
q
M M IN IN
CO CO -t
totovovq t^oooq qv
<N <N <N
IN
'
IN <N
IN <N
INCS<NNC<01NCO
COCOtOtOCOtOtOtO
cOcocococOtOtOtO
IN 0 Ov
» c- c^
0 a 000
to 0 -to 0 to CM t^
8
M IN 00
w "to
to CO 0^ -to r^ t^ t
0 -o
cs r^
0 IN
CO to
IN 00 M tOOO 0 0
0 -to -to coo CO
OD tOM to
OVM M
C<MOOtoOtt~-Ov
ONtsoOOv'ttOv
?) tio
0 00
c< 0
10 to
W to 0 M
r- 0> to
m Ov ^
IN OlO ■*
0 d 0 M IN 4^ 0.
.i3 0 to 0
to MOO
vocOM OvOOOOOOOO
0 w to
vO 00 0^
M to lOt^
OvM co>or>-0>M CO
OOO M coo 00 M to
0 Ov c^ t r- 0 too
"^
IN <N
to to
CO to
'^ttttt'C"?
100. ^ q 0 r-. t-.
t-. t-~a5oqoo Ov Ov Ov
—
a>,-*
Hf n:f a.t t-t'4
»■» <-!•*
wn. a,-* -^-c nif
S3 n.s
no
no
*0 iOU
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lOr OS tew coo
■ON
NW
Jo
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10c « =
t-W
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"
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«!«> Nm iHH CW
^
t^ cvn rir* nn
sq;ino}-Axis o) saoipBj j pappy
490
GENERAL REFERENCE TABLES
Decimal Equivalents, Squares, Square Roots, Cubes and Cube
Roots of Fractions; Circumferences and Areas of Cir-
cles FROM 6^4f to I inch
Frac-
tion
Dec.
Equiv.
Square
Sq.
Root
Cube
Cube
Root
Circum.
Circle
Area
Circle
->
.015625
.03125
.046875
.0625
.000244
.0009765
.002197
.003906
.1250
.1768
.2165
.2500
.000003815
.00003052
.000103
.0002442
.2500
.3150
.3606
.3968
,04909
.09818
•1473
•1963
.000192
.000767
.001726
.003068
A
A
t
.078125
.09375
.109375
.1250
.006104
.008789
.01196
•01563
.2795
.3062
•3307
.3535
.0004768
.0008240
.001308
.001953
•4275
•4543
.4782
.5000
•2455
•2945
•3436
•3927
.004794
.006903
.009396
.01228
1
.140625
.15625
.171875
.1875
.01978
.02441
.02954
•03516
•3750
•3953
.4161
•4330
.002781
.003815
.005078
.006592
.5200
•5386
•5560
.5724
.4438
.4909
.5400
.5890
•01553
.01916
.02321
.02761
if
.203125
.21875
.234375
.2500
.04126
.04786
•05493
.0625.
•4507
.4677
.4841
.5000
.008381
.01047
.01287
.01562
.5878
.6025
.6166
.6300
.6381
.6872
.7363
.7854
.03241
.03758
.04314
.04909
.265625
.28125
.296875
•3125
.07056
.07910
.08813
•0976.6
•5154
•5303
.5449
.5590
.01874
.02225
.02616
.03052
.6428
•6552
.6671
.6786
.8345
.8836
.9327
.9817
.05541
.06213
.06922
.07670
f
.328125
•34375
•359375
•3750
.1077
.1182 '
.12913
.1406
.5728
.5863
.5995
.6124
.03533
.04062
.04641
.05273
.6897
.7005
.7110
.7211
1. 03 1
1.080
1. 129
1. 178
.08456
.09281
.1014
.1104
If
.390625
.40625
.421875
•4375
.1526
.1650
.17800
.1914
.6250
•6374
.6495
.6614
.05960
,06705
.07508
.08374
.7310
.7406
.7500
.7592
1.227
1.276
1-325
1-374
.1226
.1296
.1398
.1503
ft
II
•453125
.46875
.484375
.5000
.2053
.2197
.2346
.2500
.6732
.6847
.6960
.7071
.09304
.1030
.1136
.1250
.7681
.7768
.7853
.7937
1.424
T.473
1.522
1.571
.1613
.1726
.1843
.1963
SQUARES, CUBES AND ROOTS
491
Decimal Equivalents, Squares, Square Roots, Cubes, Cube
Roots of Fractions; Circumferences and Areas of Cir-
cles FROM T-^ TO I inch.
Frac-
tion
Dec.
Equiv.
Square
Sq.
Root
Cube
Cube
Root
Circum.
Circle
Area
Circle
1
•515625
•53125
•546875
•5625
•2659
.2822
.2991
.3164
.7181
.7289
•7395
.7500
•1371
.1499
.1636
.1780
.8019
.8099
.8178
•8255 •
1.620
1.669
1.718
1.767
.2088
.2217
.2349
.2485
f
•578125
•59375
•609375
.6250
•3342
•3525
•3713
.3906
.7603
.7706
.7806
.7906
.1932
.2093
.2263
.2441
•8331
•8405
.8478
•8550
1.816
1.865
1.914
1.963
•2625
.2769
.2916
.3068
If
.640625
.65625
.671875
.6875
.4104
•4307
•4514
.4727
.8004
.8101
.8197
.8292
.2629
.2826
-3^33
•3250
.8621
.8690
•8758
.8826
2.013
2.062
2. Ill
2.160
•3223
•3382
•3545
.3712
If
If
f
.703125
•71875
•734375
.7500
•4944
.5166
•5393
•5625
•8385
.8478
.8^69
.8660
•3476
•3713
.3961
.4219
.8892
•8958
.9022
.Q086
2.209
2.258
2.307
2^356
.3883
•4057
.4236
.4418
II
•765625
.78125
.796875
.8125
.5862
.6104
•6350
.6602
.8750
.8839
.8927
.9014
.4488
.4768
.5060
•5364
.9148
.9210
.9271
•9331
2.405
2.454 '
2.503
2^553
.4604
•4794
.•4987
•5185
ft
.828125
•84375
•859375
.8750
.6858
.7119
•7385
.7656
.9100
.9186
.9270
•9354
•5679
.6007
•6347
.6699
•9391
•9449
•9507
•9565
2.602
2.651
2.700
2.749
•5386
•5592
.5801
.6013
If
.890625
.90625
.921875
•9375
•7932
.8213
.8499
.8789
•9437
.9520
.9601
.9682
.7064
•7443
•7835
.8240
.9621
.9677
•9732
•9787
2.798
2.847
2.S96
2-945
.6230
.6450
.6675
•6903
If
I
•953125
.96875
•984375
I
.9084
•9385
.9690
I
•9763
.9843
.9922
I
.8659
.9091
•9539
I
.9841
•9895
•9948
I
2.994
3-043
3-093
3-1416
•713s
.7371
.7610
.7854
492
GENERAL REFERENCE TABLES
Squares, Cubes, Square and Cube Roots of Numbers from
I TO lOOO
No.
Square
Cube'
Sq.
Root
Cube
Root
No.
Square
Cube
Sq.
Root
Cube
Root
I
I
I
1. 0000
1. 0000
51
2601
132651
7.1414
3-7084
2
4
8
1.4142
1-2599
52
2704
140608
7
2111
3-7325
3
9
27
1. 7321
1.4422
53
2809
148877
7
2801
3-7563
4
16
64
2.0000
1-5874
54
2916
157464
7
3485
3-7798
25
I2>
2.2361
I. 7100
55
3025
166375
7
4162
3.8030
6
36
216
2.4495
1.8171
56
3136
175616
7
4833
3-8259
7
49
343
2.6458
1. 9129
57
3249
185193
7
5498
3-8485
8
64
512
2.8284
2.0000
58
3364
195112
7
6158
3.8709
Q
81
729
3.0000
2.0801
59
3481
20S379
7
6811
3-8930
lO
100
1000
3.1623
2.1544
60
3600
216000
7-7460
3-9149
II
121
133 1
3-3166
2.2240
61
3721
226981
7.8102
3.9365
12
144
1728
3.4641
2.2894
62
3844
23S328
7.8740
3-9579
13
i6q
2197
3.6056
2.3513
63
3969
250047
7.9373
3-9791
14
196
2744
3-7417
2.4101
64
4096
262144
8.0000
4.0000
15
225
3375
3-8730
2.4662
65
4225
274625
8.0623
4.0207
i6
256
4.0000
2.5198
66
4356
287496
8.1240
4.0412
17
289
4913
4.1231
2.5713
67
4489
300763
8.1854
4-0615
i8
324
5832
4.2426
2.6207
68
4624
314432
8.2462
4.0817
19
361
6859
4-3589
2.6684
69
4761
328509
8.3066
4.1016
20
400
8000
4-4721
2.7144
70
4900
343000
8.3666
4.1213
21
441
9261
4.5826
2.7589
71
5041
357911
8.4261
4.1408
22
484
10648
4.6904
2.8020
72
5184
373248
8.4853
4.1602
23
529
12167
4-7958
2.8439
73
5329
389017
8.5440
4-1793
24
576
13824
4;8990
2.8845
74
5476
405224
8.6023
4.1983
25
625
15625
5.0000
2.9240
75
5625
421875
8.6603
4-2172
26
676
17576
5-0990
2.9625
76
5776
438976
8.7178
4-2358
27
729
19683
S-1962
3.0000
77
5929
456533
8.7750
4-2543
28
784
21952
5-2915
3-0366
78
6084
474552
8.8318
4.2727
29
841
24389
5-3852
3-0723
79
6241
493039
8.8882
4.2908
30
900
27000
5-4772
3-1072
80
6400
512000
8.9443
4-3689
31
961
29791
5-5678
3-1414
81
6561
531441
9.0000
4.3267
32
1024
32768
5-6569
3-1748
82
6724
551368
9-0554
4-3445
33
1089
35937
5-7446
3.2075
83
6889
571787
9.1 104
4-3621
34
1156
39304
5-8310
3-2396
84
7056
592704
9.1652
4-3795
35
1225
42875
5.9161
3.2711
85
7225
614125
9.2195
4-3968
36
1296
46656
6.0000
3-3019
86
7396
636056
9.2736
4.4140
37
1369
50653
6.0828
3-3322
87
7569
658503
9.3276
4-4310
38
1444
54872
6.1644
3.3620
88
7744
681472
9-3808
4.4480
39
1521
59319
6.2450
3.3912
89
7921
704969
9-4340
4-4647
40
1600
6.3246
3.4200
90
8100
729000
9.4868
4-4814
41
1681
68921
6.4031
3-4482
91
8281
753571
9-5394
4-4979
42
1764
74088
6.4807
3-4760
92
8464
778688
9-5917
4-5144
43
1849
79507
6.5574
3-5034
93
8649
804357
9-6437
4-5307
44
1936
85184
6.6332
3-5303
94
8836
830584
9-6954
4-5468
45
2025
91125
6.7082
3-5569
95
9025
857375
9.7468
4-5629
46
2116
97336
6.7823
3.5830
96
9216
884736
9.7980
4-5789
i.l
2209
103823
6.8557
3.6088
97
9409
912673
9.8489
4-5947
48
2304
I 10592
6.9282
3-6342
98
9604
941192
9-8995
4.6104
49
2401
I I 7649
7.0000
3-6593
99
9801
970299
9.9499
4.6261
SO
2500
125000
7.0711
3-6840
100
lOOOO
I 000000
10.0000
4.6416
SQUARE, CUBES AND ROOTS
493
Squares, Cubes, Square and Cube Roots of Numbers from
I TO lOOO
No.
Square
Cube
Sq.
Root
Cube
Root
No.
Square
Cube
Sq.
Root
Cube
Root
lOI
10201
1030301
10.0499
4.6570
151
22801
3442951
12.2882
5.3251
I02
10404
1061208
10.0995
4-6723
152
23104
3511808
12.3288
-3368
103
10609
1092727
10.14S9
4.687s
IS3
23409
3581577
12.3693
.3485
104
10816
1 1 24864
10.1980
4.7027
154
23716
3652264
12.4097
.3601
105
II02S
1157625
10.2470
4-7177
155
24025
3723875
12.4499
.3717
106
11236
1191016
10.2956
4.7326
156
24336
3796416
12.4900
.3832
107
1 1 -149
1225043
10.3441
4.747s
157
24649
3869893
12.5300
.3947
108
1 1 664
1259712
10.3923
4.7622
158
24964
3944312
12.5698
4061
109
11881
1295029
10.4403
4-7769
159
25281
4019679
12.6095
4175
IIO
1 2 100
133 1000
10.4881
4.7914
160
25600
4096000
12.6491
4288
III
12321
1367631
10.5357
4.8059
161
25921
4173281
12.6886
S.4401
112
12544
1404928
10.5830
4-8203
162
26244
4251528
12.7279
5
4514
113
12769
1442897
10.6301
4.8346
163
26569
4330747
12.7671
5
4626
114
12996
1481544
10.6771
4.8488
164
26896
4410944
12.8062
S
4737
115
1322s
1520875
10.7238
4.8629
165
27225
4492125
12.8452
5
4848
116
13456
1560896
10.7703
4.8770
166
27556
4574296
12.8841
5
4959
117
13689
1601613
10.8167
4.8910
167
278S9
4657463
12.9228
5
5069
118
13924
1643032
10.8628
4.9049
168
28224
4741632
12.9615
5
5178
119
14161
1685159
10.9087
4.9187
169
28561
4826809
13.0000
S
5288
120
14400
1728000
I0.9S45
4.9324
170
28900
4913000
13.0384
5
5397
121
14641
1771561
11.0000
4.9461
171
29241
50002 I I
13.0767
5.5505
122
14884
1815848
11.0454
4-9597
172
29584
S088448
13.1149
5
5613
123
15129
1860867
11.0905
4-9732
173
29929
5177717
13.1529
5
5721
124
15376
1906624
11.1355
4-9866
174
30276
526S024
13.1909
5
5828
125
15625
195312s
II. 1803
5.0000
17s
30625
5359375
13.2288
5
5934
126
15876
2000376
11.2250
5-013.3
176
30976
5451776
13.2665
5
6041
127
16129
2048383
11.2694
. 5.0265
177
31329
5545233
13.3041
5
6147
128
16384
2097152
11.3137
5.0397
178
31684
5639752
13-3417
5
6252
129
16641
2146689
11.3578
5.0528
179
32041
5735339
13.3791
5
6357
130
16900
2197000
II. 4018
5.0658
180
32400
5832000
13.4164
S
6462
131
17161
2248091
II.44SS
5.0788
181
32761'
5929741
13.4536
5.6567
132
17424
2299968
II. 4891
5.0916
182
33124
6028568
13.4907
S
6671
133
17689
2352637
11.5326
5.104s
183
33489
■6128487
13-5277
5
6774
134
17956
2406104
11.5758
5.1172
184
33856
6229504
13.5647
S
6877
135
18225
2460375
II. 6190
5.1299
185
34225
6331625
13.6015
5
6980
136
18496
2515456
II. 6619
5.1426
186
34596
6434856
13.6382
S
7083
137
18769
2571353
11.7047
S-1551
187
34969
6539203
13-6748
5
7185
138
19044
2628072
11-7473
5-1676
188
35344
6644672
13 -7 1 13
5
7287
139
19321
2685619
11.7898
S-i8oi
189
35721
6751269
13-7477
5
7388
140
19600
2744000
11.8322
5-1925
190
36100
6859000
13.7840
5
7489
141
1 988 1
2803221
11.8743
S-2048
191
36481
6967S71
13.8203
5.7590
142
20164
2863288
II. 9164
5.2171
192
36864
7077888
13.8564
5.7690
143
20449
2924207
11.9583
S.2293
193
37249
7189057
13.8924
5.7790
144
20736
2985984
12.0000
5.241S
194
37636
7301384
13-9284
S.7890
145
21025
3048625
12.0416
5.2536
195
38025
7414875
13-9642
5.7989
146
2 13 16
3112136
12.0830
5.2656
196
38416
7529536
14.0000
5.8088
147
21609
3176523
12.1244
5.2776
197
38809
7645373
14-0357
5-8186 _
148
21904
3241702
12.1655
5.2896
198
39204
7762392
14.0712
5-8285
149
22201
3307949
12.2066
S-3015
199
39601
7880599
14.1067
5.8383
ISO
22500
337SOOO
12.2474
5-3133
200
40000
8000000
14.1421
5.8480
494
GENERAL REFERENCE TABLES
Squares, Cubes, Square and Cube Roots of Numbers from
I TO lOOO
No.
Square
Cube
Sq.
Root
Cube
Root
No.
Square
Cube
Sq.
Root
Cube
Root
20I
40401
81 20601
14.1774
5-8578
251
63001
15813251
15-8430
6.3080
202
40804
8242408
14.2127
5-8675
252
63504
16003008
15-8745
6.3164
203
41209
8365427
14.2478
5-8771
253
64009
16194277
15.9060
6.3247
204
41616
84S9664
14.2829
S.8868
254
64516
16387064
15-9374
6.3330
20s
42025
8615125
14.3178
5-8964
255
6502s
16581375
15-9687
6.3413
206
42436
8741816
14-3527
5-9059
256
65536
16777216
16.0000
6.3496
207
42849
8869743
14-3875
5-9155
257
66049
16974593
16.0312
6.3579
208
4^264
8998912
14-4222
5-9250
258
66564
17173512
16.0624
6.3661
209
43681
9129329
14-4568
5-9345
259
67081
17373979
16.093s
•6.3743
210
44100
9261000
14.4914
5-9439
260
67600
17576000
16.1245
6.382s
211
44521
9393931
14-5258
5-9533
261
68121
17779581
16.1555
6.3907
212 44944
9528128
14.5602
5-9627
262
68644
17984728
16.1864 6.3988
213 45369
9663597
14- 5945-
5-9721
263
69169
18191447
16.2173 6.4070
214 45796
9800344
14.6287
5-9814
264
69696
18399744
16.2481 6.4151
215 46225
9938375
14.6629
5-9907
265
70225
18609625
16.2788 6.4232
216 46656
10077696
14.6969
6.0000
266
70756
18821096
16.309s
6.4312
217
47089
10218313
14.7309
6.0092
267
71289
19034163
16.3401
6.4393
218
47524
10360232
14.7648
6.0185
268
71824
19248832
16.3707
6.4473
219
47961
10503459
14.7986
6.0277
269
72361
19465109
16.4012
6.4553
220
48400
10648000
14-8324
6.0368
270
72900
19683000
16.4317
6.4633
221
48841
10793861
14.8661
6.0459
271
73441
19902511
16.4621
6.4713
222 49284
1094 1 048
14.8997
6.0550
272
73984
20123648
16.4924
6.4792
223 49729
I 1089567
14.9332
6.0641
273
74529
20346417
16.5227
6.4872
224! 50176
11239424
14.9666
6.0732
274
75076
20570824
16.5529
6.4951
225!. 50625
11390625
15.0000
6.0822
275
7562s
20796875
16.5831
6.5030
226' 51076
11543176
15-0333
6.0912
276
76176
21024576
16.6132
6.5108
227! S1529
I 1697083
15.0665
6.1002
277
76729
21253933
16.6433
6.5187
228: 51984
11852352
15.0997
6.1091
278
77284
21484952
16.6733
6.5265
229' 52441
12008989
15-1327
6.1180
279
77841
21717639
16.7033
6.5343
230 52900
I 2 167000
15-1658
6.1269
280
78400
21952000
16.7332
6.5421
231 53361
12326391
15.1987
6.1358
281
78961
22188041
16.7631
6.5499
232 53824
1 2487 168
15-2315
6.1446
282
79524
22425768
16.7929
6-5577
233 54289
12649337
15.2643
6.1534
283
80089
22665187
16.8226
6.5654
234 54756
12812904
15.2971
6.1622
284
80656
22906304
16.8523
^.■H^l
235 55225
12977875
15-3297
6.1710
285
8122s
23149125
16.8819
6.5808
236 55696
13144256
15-3623
6.1797
286
81796
23393656
16.9115
6.5885
237 56169
133 1 2053
15-3948
6.1885
287
82369
23639903
16.9411
6.5962
238 56644
13481272
15.4272
6.1972
288
82944
23887872
16.9706
6.6039
239 57121
13651919
15.4596
6.2058
289
83521
24137569
17.0000
6.611S
240 57600
13824000
15.4919
6.214s
290
84100
24389000
17.0294
6.6191
241 58081
13997521
15.5242
6.2231
291
84681
24642171
17.0587
6.6267
242 58564
14172488
15-5563
6.2317
292
85264
24897088
17.0880
6.6343
243 59049
14348907
15.5885
6.2403
293
8S849
25153757
17.1172
6.6419
244 59536
14526784
15.6205
6.248S
294
86436
25412184
17.1464
6.6494
245 60025
14706125
15.6525
6.2573
295
87025
25672375
17.1756
6.6569
246 60516
148S6936
15.6844
6.2658
296
87616
25934336
17.2047
6.6644
247 61009
15069223
15.7162
6.2743
297
88 209
26198073
17.2337
6.6719
248 61504
15252992
15.7480
6.2828
298
88804
26463592
17.2627
^^^?4
249 62001
15438249
15-7797
6.2912
2-3
89401
26730899
17.2916
6.6869
250 62500
15625000
15.8114
6.2996
300
90000
27000000
17.320S
6.6943
SQUARES, CUBES AND ROOTS
495
Squares, Cubes, Square and Cube Roots of Numbers from
I TO lOOO
No.
Square
Cube
Sq.
Root
Cube
Root
No.
Square
Cube
Sq.
Root
Cube
Root
301
90601
27270901
17.3494
6.7018
351
123201
43243551
18.7350
7.0540
302
91204
27543608
17.3781
6.7092
352
123904
43614208
18.7617
7.0607
303
91809
27818127
17.4069
6.7166
353
124609
43986977
18.7883
7.0674
304
92416
28094464
17-4356
6.7240
354
125316
44361864
18.8149
7.0740
305
93025
28372625
17.4642
6.7313
355
126025
44738875
18.8414
7.0807
306
93636
28652616
17.4929
6.7387
356
126736
45118016
18.8680
7.0873
307 1 94249
28934443
17.5214
6.7460
357
127449
45499293
18.8944
7.0940
308^ 94864
29218112
17.5499
6.7533
358
128164
45882712
18.9209
7.1006
3091 95481
29503629
17.5784
6.7606
359
128881
46268279
18.9473
7.1072
310
96100
29791000
17.6068
6.7679
360
129600
46656000
18.9737
7.1138
311
96721
30080231
17.6352
6.7752
361
130321
47045881
19.0000
7.1204
312
97344
30371328
17.6635
6.7824
362
131044
47437928 19.0263
7.1269
313
97969
30664297
17.6918
6.7897
363-
131769
47832147 19.0526
7.1335
314
98596
30959144
17.7200
6.7969
364
132496
48228544 19.0788
7.1400
315
99225
31255875
17.7482
6.8041
365
133225
4862712s
19.1050
7.1466
316
99856
31554496
17.7764
6.8113
366
133956
49027896
19.1311
7.1531
317
100489
31855013
17.8045
6.818s
367
134689
49430863
19.1572
7.1596
318
101124
32157432
17.8326
6.8256
368
135424 49836032
19.1833
7.1661
319
101761
32461759
17.8606
6.8328
369
136161
.50243409 19.2094
7.1726
320
102400
32768000
17.888s
6.8399
370
136900
50653000
19.2354
7.1791
321
103041
33076161
17.9165
6.8470
371
137641
5 10648 I I
19.2614
7.18SS
322
103684
33386248
17.9444
6.S541
372
138384; 51478S48 19.2873
7.1920
323
104329
33698267
17.9722
6.S612
373
139129 51895117
19.3132
7.1984
324I 104976
34012224
18.00C0
6.8683
374
139876: 52313624
19.3391
7.2048
32s
105625
34328125
18.0278
6.8753
375
140625' 52734375
19.3649
7.2112
326
106276
34645976
18.0555
6.SS24
376
141376I 53157376
19.3907
7-2177
327
106929
34965783
18.0831
6.8S94
377
142129! 53582633
19.4165
.7.2240
328
107584
35287552
18.1108
6.8964
378
142884! 54010152
19.4422
7.2304"
329
108241
35611289
18.1384
6.9034
379
143641
54439939
19.4679
7.2368
330
108900
35937000
18.1659
6.9104
380
144400
54872000
19.4936
7.2432
331
109561
36264691
18.1934
6.9174
381
145161
55306341
19.5192
7.249s
332
110224
36594368
18.2209
6.9244
382
145924! 5574296S
19.5448
7.2558
333
I 10889
36926037
18.2483
6.9313
383
146689! 56181887
19.5704
7.2622
334
111556
37259704
18.2757
6.9382
384
147456, 56623104
19-5959
7.2685
335
112225
37595375
18.3030
6.9451
385
1482251 57066625
19.6214
7.2748
336
I12896
37933056
18.3303
6.9521
386
148996 57512456
19.6469
7.2811
337
113569
38272753
18.3576
6.9589
387
149769: 57960603
19.6723
7.2874
338
I 14244
38614472
18.3848
6.9658
388
150544, 5S41T072
19.6977
7.2936
339
114921
38958219
18.4120
6.9727
389
151321
58863S69
19.7231
7-2999
340
I I 5600
39304000
18.4391
6.9795
390
152100
59319000
19.7484
7.3061
341
I16281
39651821
18.4662
6.9864
391
1528S1
59776471
19.7737
73124
342
116964
40001688
18.4932
6.9932
392
153664
60236288
19.7990
7-3186
343
I I 7649
40353607
18.5203
7.0000
393
154449
60698457
19.8242
7.3248
344
118336
40707584
18.5472
7.0068
394
155236
611629S4
19.8494
7.3310
345
119025
41063625
18.5742
7.0136
395
156025
61629S75
19.8746
7.337«
346
119716
41421736
18.6011
7.0203
396
156816
62099136
19.8997
7.3434
347
1 20409
41781923
18.6279
7.0271
397
157609
62570773
19.9249
7-3496
348
121104
42144192
18.6548
7.0338
398
158404
63044792
19.9499
7.3558
349
121801
42508549
18.6815
7.0406
399
159201
6352 I 199
19.9750
7.3619
350
122500
42875000
18.7083
7-0473
400
160000
64000000
20.0000
7.3681
496
GENERAL REFERENCE TABLES
Squares, Cubes, Square and Cube Roots of Numbers from
I TO lOOO
No.
Square
Cube
Sq.
Root
Cube
Root
No.
Square
Cube
Root
Cube
Root
401
160801
64481201
20.0250
7-3742
451
203401
•91733851
21.2368
7.6688
402
161604
6496480S
20.0499
7
3803
452
204304
92345408
21.2603
7
6744
403
162409
65450827
20.0749
7
3864
453
205209
92959677
21.2838
7
6800
404
163216
65939264
20.0998
7
3925
454
206116
93576664
21.3073
7
6857
405
164025
66430125
20.1246
7
3986
455
207025
94196375
21.3307
7
6914
406
164836
66923416
20.1494
7
4047
456
207936
94818816
21.3542
7
6970
407
165649
67419143
20.1742
7
4108
457
208849
95443993
21.3776
7
7026
408
166464
67917312
20.1990
7
4169
458
209764
96071912
21.4009
7
7082
40Q
167281
68417929
20.2237
7
4229
459
210681
96702579
21.4243
7
7138
410
168100
68921000
20.2485
7.4290
460
2 I 1600
97336000
21.4476
7-7194
411
168921
69426531
20.2731
7.4350
461
212521
97972181
21.4709
7.7250
412
169744
69934528
20.2978
7
4410
462
213444
98611128
21.4942
7-7306
413
170569
70444997
20.3224
4470
463
214369
99252847
21.5174
7-7362
414
171396
70957944
20.3470
7
4530 .
464
215296
99897344
21.5407
7.7418
415
172225
71473375
20.3715
7
4590
465
216225
10054462s
21.5639
7-7473
416
173056
71991296
20.3961
7
4650
466
217156
101194696
21.5870
7.7529
417
173889
72511713
20.4206
7
4710
""^.l
218089
101847563
21.6102
7-7584
418
174724
73034632
20.4450
7
4770
468
219024
102503232
21.6333
7.7639
419
175561
73560059
20.4695
7
4829
469
219961
103161709
21.6564
7-7695
420
176400
74088000
20.4939
7
4889
470
220900
103823000
21.6795
7-7750
421
177241
74618461
20.5183
7.4948
471
221841
104487 111
21.7025
7.7805
422
178084
75151448
20.5426
7.5007
472
222784
105 I 54048
21.7256
7.7860
423
178929
75686967
20.5670
7.5067
473
223729
105823817
21.7486
7-7915
424
179776
76225024
20.5913
7.5126
474
224676
106496424
21.7715
7-7970
42s
180625
76765625
20.6155
7-5185
475
225625
107171875
21.7945
7.8025
426
181476
77308776
20.6398
7-5244
476
226576
107850176
21.8174
7-8079
427
182329
77854483
20.6640
7.5302
477
227529
108531333
21.8403
7-^'lt
428
183184
78402752
20.6882
7-5361
478
228484
1092x5352
21.8632
7.8188
429
I 8404 I
78953589
20.7123
7-5420
479
229441
109902239
21.8861
7-8243
430
184900
79507000
20.7364
7-5478
480
230400
I 10592000
21.9089
7.8297
431
185761
80062991
20.7605
7-5537
481
231361
111284641
21.9317
7.8352
432
186624
80621568
20.7846
7
5595
482
232324
111980168
21.9545
7.8406
433
187489
81182737
20.8087
7
5654
483
233289
112678587
21.9773
7.8460
434
188356
81746504
20.8327
7
5712
484
234256
113379904
22.0000
7-^514
435
189225
82312875
20.8567
7
5770
485
235225
114084125
22.0227
7-8568
436
190096
82881856
20.8806
5828
486
236196
114791256
22.0454
7.8622
437
190969
83453453
20.9045
7
5886
487
237169
115501303
22.0681
7.8676
438
191S44
84027672
20.9284
7
5944
4S8
238144
116214272
22.0907
^•Vl°
439
192721
84604519
20.9523
7
6001
489
239121
116930169
22.1133
7.8784
440
193600
85184000
20.9762
7
6059
490
240100
117649000
22.1359
7-8837
441
I 9448 I
85766121
21.0000
7.6117
491
241081
118370771
22.1585
7.8891
442
195364
86350888
21.0238
7-6174
492
242064
119095488
22.1811
7.8944
443
196249
86938307
21.0476
7-6232
493
243049
X19823157
22.2036
7.8998
444
197136
87528384
21.0713
7.6289
494
244036
120553784
22.2261
7-9051
445
19S025
88121125
21.0950
7.6346
495
245025
121287375
22.2486
7-9105
446
198916
88716536
21.1187
7-6403
496
246016
122023936
22.2711
7-9158.
447
199809
89314623
21.1424
7.6460
497
247009
122763473
22.2935
7.9211
448
200704
89915392
21.1660
7-6517
498
248004
123505992
22.3159
7.9264
449
201601
90518849
21.1896
7-6574
499
249001
124251499
22.3383
7-9317
450
202500
91125000
21.2132
7-6631
500
250000
125000000
22.3607
7.9370
SQUARES, CUBES AND ROOTS
497
Squares, Cubes, Square and Cube Roots of Numbers from
I TO lOOO
No.
Square
Cube
Sq.
Root
Cube
Root
No.
Square
Cube
Sq.
Root
Cube
Root
501
251001
125751501
22.3830
7-9423
551
303601
167284151
23.4734
8.1982
502
252004
126506008
22.4054
7.9476
552
304704
168196608
23-4947
8.2031
503
253009
127263527
22.4277
7.9528
553
305809
169112377
23.5160
8.2081
504
254016
128024064
22.4499
7-9581
554
306916
I 7003 I 464
23-5372
^•^'^°
50'5
255025
128787625
22.4722
7-9634
555
308025
170953875:23.5584
8.2180
506
256036
129554216
22.4944
7.9686
556
309136
171879616
23-5797
8.2229
507
257049
130323843
22.5167
7-9739
557
310249
172808693
23.6008
8.2278
508
258064
13 10965 I 2
22.5389
7.9791
558
311364
173741112
23.6220
8.2327
509
259081
131872229
22.5610
7.9843
559
312481
174676879
23-6432
8.2377
510
260100
13 265 1000
22.5832
7.9896
560
313600
175616000
23.6643
8.2426
511
261121
133432831
22.6053
7.9948
S6i
314721
176558481
23.6854
8.247S
512
262144
134217728
22.6274
8.0000
562
315844
177504328
23.7065
8.2524
S13
26316Q
135005697
22.6495
8.0052
563
316969
178453547
23.7276
8.2573
514
264106
135796744
22.6716
8.0104
564
318096
I 79406144
23.7487
8.2621
265225
136590875
22.6936
8.0156
565
319225
180362125
23.7697
8.2670
516
266256
1373S8096
22.7156
8.0208
566
320356
181321496
23.7908
8.2719
517
267289
13818S413
22.7376
8.0260
567
321489
182284263
23.8118
8.2768
51S
268324
138991832
22.7596
8.0311
568
322624
183250432
23.8328
8.2816
519
269361
139798359
22.7816
8.0363
569
323761
184220009
23-8537
8.286s
520
270400
140608000
22.8035
8.041 5
570
324900
185192000
23.8747
8.2913
521
271441
141420761
22.8254
8.0466
571
326041
186169411
23.8956
8.2962
522
272484
142236648
22.8473
8.0517
572
327184
187149248
23.9165
8.3010
523
273529
143055667
22.8692
8.0569
573
328329
188132517
23.9374
8.3059
524
274576
143877824
22.8910
8.0620
574
329476
189119224
23-9583
8.3107
52s
275625
144703125
22.9129
8.0671
575
330625
190109375
23.9792 8.3155
526
276676
145531576 22.9347
8.0723
576
.331776
191102976
24.0000 8.3203
527
277729
146363183:22.9565
8.0774
577
332929
192 100033
24.0208
8.3251
528
278784
147197952 22.9783
8.0825
578
334084
193100552
24.0416
8.3300
529
279841
148035889123.0000
8.0876
579
335241
194104539
24.0624
8.3348
530
280900
148877000
23.0217
8.0927
580
336400
195 1 12000
24.0832
8.3396
531
281961
149721291
23.0434
8.0978
581
337561
196122941
24.1039
8.3443
532
283024
150568768
23.0651
8.1028
582
338724
197137368
24.1247
8.3491
533
2840S9
151419437
23.0868
8.1079
583
339S89
198155287
24-1454
8.3539
534
285156
152273304
23.1084
8.1130
584
341056
199176704
24.1661
8.3587
535
286225
15313037s
23.1301
8.1180
585
342225
200201625
24.1868
8.3624
536
287296
153990656 23.1517
8.1231
586
343396 201230056
24.2074
8.3682
537
288369
154854153 23.1733
8.1281
587
344569
202262003
24.2281
8.3730
53^
289444
155720872
23.1948
8.1332
588
345744
203297472 24.2487
^•^777
539
290521
156590819
23.2164
8.1382
589
346921
204336469 24.2693
8.3825
540
291600
157464000
23.2379
8.1433
590
348100
205379000
24.2899
8.3872
541
292681
I 5834042 I
23.2594
8.1483
591
349281
206425071
24-310S
8.3919
542
293764
159220088
23.2809
8.1533
592
350464
207474688
24-3311
8.3967
543
294849
160103007 23.3024
8.1583
593
351649
208527857
24-3516
8.4014
544
295936
160989184
23.3238
8.1633
594
352836
209584584
24.3721
8.4061
545
297025
161878625
23.3452
8.1683
595
35402s
210644875
24.3926
8.4108
546
298116
162771336
23.3666
8.1733
596
355216
211708736
24.4131
8.41SS
547
299209
163667323
23.3880
8.1783
597
356409
212776173
24-4336
8.4202
548
300304
164566592
23.4094
8.1833
598
357604
213847192
24.4540
8.4249
549
301401
165469149
23-4307
8.1882
599
358801
214921799
24-4715
8.4296
550
302500
166375000
23.4521
8.1932
600
360000
216000000
24.4949
8.4343
498
GENERAL REFERENCE TABLES
Squares, Cubes, Square and Cube Roots of Numbers from
I TO lOOO
No.
Square
Cube
Sq.
Root
Cube
Root
No.
Square
Cube
Sq.
Root
Cube
Root
6oi
361 201
217081801
24-5153
8.4390
651
423801
275894451
25.5147
8.6668
602
362404
218167208
24-5357
8.4437
652
425104
277167808
25-5343
8.6713
603
363609
219256227
24.5561
8.4484
653
426409
278445077
25-5539
8.6757
604
364816
220348864
24-5764
8.4530
654
427716
279726264
25-5734
8.6801
605
366025
221445125
24.5967
8.4577
655
429025
281011375
25-5930
8.6845
606
367236
222545016
24.6171
8.4623
656
430336
282300416
25.6125
8.6890
607
368449
223648543
24-6374
8.4670
657
431649
283593393
25.6320
8.6934
608
369664
224755712
24.6577
8.4716
658
432964
284890312
25-6515
8.6978
609
370881
225866529
24.6779
8.4763
659
434281
286191179
25.6710
8.7022
610
372100
226981000
24.6982
8.4809
660
435600
287496000
25.690s
8.7066
611
373321
228099131
24.7184
8.4856
661
436921
288804781
25-7099
8.7110
612
374544
229220928
24.7386
8.4902
662
438244
290117528
25.7294
8.7154
613
375769
230346397
24.7588
8.4948
663
439569
291434247
25.7488
8.7198
614
376996
231475544
24.7790
8.4994
664
440896
292754944
25.7682
8.7241
6iS| 378225
232608375
24.7992
8.5040
665
442225
294079625
25.7876
8.728s
616 379456
233744896
24.8193
8.5086
666
443556
295408296
25.8070
8.7329
6171 380689
234885113124.8395
8.5132
667
444889
296740963
25.8263
8.7373
6181 381924
236029032
24.8596
8.5178
668
446224
298077632
25.8457
8.7416
619! 383161
237176659
24.8797
8.5224
669
447561
299418309
25.8650
8.7460
620
384400
238328000
24.8998
8.5270
670
448900
300763000
25.8844
8.7503
621
385641
239483061
24.9199
8.5316
671
450241
302111711
25.9037
8.7547
622
386884
240641848
24-9399
8.5362
672
451584
303464448
25.9230
8.7590
623
388129
241804367
24.9600
8.5408
673
452929
304821217
25.9422
8.7634
624
389376
242970624
24.9800
8.5453
674
454276
306182024
25.9615
8.7677
625
.^90625
244140625
25.0000
8.5499
675
455625
307546875
25.9808
8.7721
626 391876
245314376
25.0200
8.5544
676
456976
308915776
26.0000
8.7764
627I 393129
246491S83
25.0400
8.5590
677
458329
310288733
26.0192
8.7807
628, 394384
247673152
25-0599
8.5635
678
459684
311665752
26.0384
8.7850
629] 395641
248858189125.0799
8.5681
679
461041
313046839
26.0576
8.7893
630
396900
250047000
25.0998
8.5726
680
462400
314432000
26.0768
8.7937
631
398161
251239591
25.1197
8.5772
681
463761
315821241
26.0960
8.7980
632
399424
252435968125.1396
8.5817
682
465124
317214568 26.1151
8.8023
633
400689
253636137 25.1595
8.5862
683
466489
318611987 26.1343
8.8066
634, 401956
254840104I25.1794
8.5907
684
467856
320013504; 26.1534
8.8109
63S1 40322.S
256047875125-1992
8.5952
685
469225
321419125 26.1725
8.8152
636
404496
257259456125.2190
8.5997
686
470596
322828856 26.1916
8.8194
637
405769
25S474853'25.2389
8.6043
687
471969
324242703 26.2107
8.8237
638
407044
259694072,25.2587
8.6088
688
473344
325660672 26.2298
8.8280
639
408321
260917119 25.2784
8.6132
689
474721
327082769
26.2488
8.8323
640
409600
262144000 25.2982
8.6177
690
476100
328509000
26.2679
8.8366
641
410881
263374721 25.3180
8.6222
691
477481
329939371
26.2869
8.8408
642
412164
264609288125
3377
8.6267
692
478864
331373888
26.3059
8.8451
643
413449' 265847707I25
3574
8.6312
693
480249
332812557
26.3249
8.8493
644
414736I 267089984 25
3772
8.6357
694
481636
334255384
26.3439
8.8536
645
416025 26S336125 25
3969
1 8.6401
695
483025
335702375
26.3629
8.8578
646
417316 26958613625
416s
{ 8.6446
696
484416
337153536
26.3818
8.8621
647
1 418609 270840023 25
4362
' 8.6490
697
485809
338608873
26.4008
8.8663
648
419904 272097792 25
4558
8.6535
698
487204
340068392
26.4197
8.8706
649
421201 273359449 25
4755
■ 8.6579
699
488601
341532099
26.4386
8.8748
650
422500 27462500025.4951
j 8.6624
700
490000
343000000
26.4575
8.8790
SQUARES, CUBES AND ROOTS
499
Squares. Cubes, Square and Cube Roots of Numbers from
I to iooo
No.
Square
Cube
#0%
Cube
Root
No.
Square
Cube
Sq.
Root
Cube
Root
701
491401
344472101
26.4764
8.8833
751
564001
423564751
27.4044
9.0896
702
492804
345948408
26.4953
8.8875
752
565504
425259008
27.4226
9-0937
703
494209
347428927
26.5141
8.8917
753
567009
426957777
27.4408
9.0977
704
495616
348913664
26.5330
8.8959
754
568516
428661064
27.4591
9.1017
705
497025
350402625
26.5518
8.9001
755
570025
43036887s
27.4773
9.1057
706
498436
351S95816
26.5707
8.9043
756
571536
432081216
27-4955
9.1098
707
499849
353393243
26.5895
8.908s
757
573049
433798093
27.5136
9-1138
708
501264
354894912
26.6083
8.9127
758
574564
435519512
27.5318
9.1178
709
S02681
356400829
26.6271
8.9169
759
576081
437245479
27.5500
9.1218
710
504100
3S79IIOOO
26.6458
8.9211
760
577600
438976000
27.5681
9-1258
711
505521
359425431
26.6646
8.9253
761
579121
440711081
27.5862
9.1298
712
506944
360944128
26.6833
8.9295
762
580644
442450728
27.60-13
9-13^8
713
508369
362467097
26.7021
8.9337
763
582169
444194947
27.6225
9-1378
714
509796
363994344
26.7208
8.9378
764
583696
445943744
27.6405
9.1418
71S
511225
365525875
26.739s
8.9420
765
585225
44769712s
27.6586
9-1458
716
512656
367061696
26.7582
8.9462
766
586756
449455096
27.6767
9.1498
717
514089
36S601813
26.7769
S.9503
767
588289
451217663
27.6948
9-1537
718
515524
370146232
26.7955
8.9545
768
589824
452984832 27.7128
9-1577
719
516961
371694959
26.8142
8.9587
769
591361
454756609
27-7308
9.1617
720
518400
373248000
26.8328
8.9628
770
592900
456533000
27.7489
9-i6s7
721
519841
374805361
26.8514
8.9670
771
594441
458314011
27.7669
9.1696
722
521284
376367048
26.8701
8.9711
772
595984
460099648
27.7849
9.1736
723
522729
377933067
26.8887
8.9752
773
597529
461889917
27.8029
9-1775
724
524176
379503424
26.9072
8.9794
774
599076
463684824
27.8209
9.1815
725
52562s
381078125
26.9258
8.9835
775
60062s
465484375
27.8388
9-1855
726
527076
382657176
26.9444
8.9876
776
602176
467288576
27.8568
9.1894
727
528529
384240583
26.9629
8.9918
777
603729
469097433
27.8747
9-1933
728
529984
385828352
26.9S1S
8.9959
778
605284
470910952
27.8927
9-1973
729
531441
387420489
27.0000
9.0000
779
606841
472729139
27.9106
9.20I2
730
532900
389017000
27.01S5
9.0041
780
608400
474552000
27.9285
9.2052
731
534361
390617891
27.0370
9.0082
781
609961
476379541
27.9464
9.2091
732
535824
392223168
27.0555
9.0123
782
611524
478211768
27-9643
9-2130
733! 537289! 393832837
27.0740
9.0164
783
613089
480048687
27.9821
9.2170
73^
538756 395446904
27.0924
9.0205
7S4
614656
481890304
28.0000
9.2209
735
540225 397065375
27.1109
9.0246
785
616225
48373662s
28.0179
9.2248
736
541696 398688256
27.1293
9.0287
786
617796
485587656
2S.0357
9.2287
737
543169 400315553
27.1477
9.0328
787
619369
487443403
28.0535
9-2326
738
544644
401947272
27.1662
9.0369
788
620944
4S9303872
28.0713
9-2365
739
5461 21
403583419
27.1846
9.0410
789
622521
49 I I 69069
28.0S91
9.2404
740
547600
405224000
27.2029
9.0450
790
624100
493039000
28.1069
9-2443
741
549801
406869021
27.2213
9.0491
791
625681
494913671
28.1247
9.2482
742
550564
408518488
27.2397
9-0532
792
627264
496793088
28.1425
9.2521
743
552049
410172407
27.2580
9.0572
703
62SS-19
498677257
28.1603
9-2560
744
553536
411830784
27.2764
9.0613
794
630436
500566184
28.1780
9-2599
745
555025
413493625
27.2947
9.0654
795
632025
502459875
28.1957
9-2638
746
556516
415160936
27.3130
9.0694
796
633616
504358336
28.2135
9.2677
747
558009
416832723
27.3313
9.0735
797
635209
506261573
28.2312
9.2716
748
559504
418508992
27.3496
9.0775
798
636804
508169592
28.2489
9-2754
749
561001
420189749
27.3679
9.0816
799
638401
S10082399
28.2666
9-2793
750
562500
421875000J27.3861
9.0856
800
640000
512000000
28.2843
9.2832
Soo
GENERAL REFERENCE TABLES
Squares, Cubes, Square and Cube Roots of Numbers from
I to iooo
No.
Square
Cube
Sq.
Root
Cube
Root
i
No.
Square
Cube
Sq.
Root
Cube
Root
8oi
641601
513922401
28.3019
9.2870
851
724201
616295051
29.1719 9-4764
802
643204
51584Q60S
28.3196
9.2909
852
725904
618470208
29.1890 9.4801
803
644809
517781627
28.3373
9.2948
853
727609
620650477
29. 2062 j 9.4838
804
646416
519718464
28.3549
9.2986
854
729316
622835864
29.2233
9-4875
805
64802s
521660125
28.3725
9.3025
855
731025
625026375
29.2404
9.4912
806
649636
523606616
28.3901
9.3063
856
732736
627222016
29-2575
9-4040
807
651249
525557943
28.4077
9.3102
857
734449
629422793129-2746
9.4986
808
652864
52751J112
28.4253
9.3140
858
736164
631628712 29.2916
9.5023
809
654481
529475129
28.^429
9.3179
859
737881
633839779
29-3087
9.5060
810
656100
531441000
28.4605
9.3217
860
739600
636056000
29-3258
9-5097
811
657721
533411731
28.4781
9.3255
861
741321
638277381
29-3428
9-5134
812
65Q344
5353S7328
28.4956
9-3294
862
743044
640503928
29-3598! 9-5171
813
660969
537367797
28.5132
9.3332
863
744769
642735647
29.3769 9.5207
814
662596
539353144
28.5307
9.3370
864
746496
644972544
29-3939! 9-5244
815
664225
541343375
28.5482
9.3408
865
748225
647214625
29.4109 9.5281
816
665856
543338496
28.5657
9.3447
866
749956
649461896
29.4279 9.5317
817
667489
545338513
28.5832
9.3485
867
751689
651714363
29.4449 0-5354
818
669124
547343432
28.6007
9.3523
868
753424
653972032
29.4618 9-5391
819
670761
549353259
28.6182
9.3561
869
755161
656234909
29.47881 9-5427
820
672400
551368000
28.6356
9-3599
870
756900
658503000
29-4958 9-5464
821
674041
553387661
28.6531
9-3637
871
758641
6607 763 II
29.5127 9-5501
822
675684
555412248
28.6705
9.3675
872
760384
663054848
29.5296: 9.5537
823
677329
557441767
28.6880
9.3713
873
762129
665338617
29.5466; 9-5574
824
678976
559476224
28.7054
93751
874
763876
667627624
29-5635! 9-5610
825
680625
561515625
28.7228
9.3789
875
765625
669921875
29.5804I 9-5647
826
682276
563559976
28.7402
9.3827
876
767376
672221376
29-5973; 95683
827
683929
565609283
2S.7576
9.3865
877
769129
674526133
29.6142] 9-5719
828
685584
567663552
28.7750
9.3902
878
770884
676836152
29.6311 9-5756
829
687241
569722789
28.7924
9-3940
879
772641
679151439
29-6479 9-5792
830
688900
571787000
28.8097
9.3978
880
774400
681472000
29.6648
9-5828
831
690561
573856191
28.8271
9.4016
881
776161
683797841
29.6816
0.5865
832
692224
575930368
28.8444
9.4053
882
777924
686128968
29.6985
9-5901
833
693889
578009537
28.8617
9.4091
883
779689
68'8465387
29-7153 9-5937
834
695556
580093704
28.8791
9.4129
884
781456
690807104
29.7321 9-5973
835
697225
582182875
28.8964
9.4166
885
783225
693154125129-7489 0-6010
836
69S896
584277056
28.9137
9-4204
886
784996
695506456 29.7658 9.6046
837
700569
586376253
28.9310
9.4241
887
786769
697864103 29.7825; 9.6082
838
702244
588480472
28.9482
9.4279
888
788544
700227072 29.7993; 9.6118
83Q
703921
590589719
28.9655
9.4316
889
790321
702505369
29.8161
9-6154
840
705600
592704000
28.9828
9.4354
890
792100
704969000
29-8329
9.6190
841
707281
594823321
29.0000
0.4391
891
793881
707347971
29.8496
9.6226
842
708964
596947688
29.0172
9.4429
892
795664
709732288
29-8664
9.6262
843
710649
599077107
29.0345
9.4466
893
797449
712121957
29.8831
9.6298
844
712336
601211584
29.0517
0.4503
894
799236
714516984
29.8998
9-6334
845
714025
603351125
29.0689
9.4541
895
801025
716917375
29.9166
9.6370 j
846
715716
605405736
29.0861
9-4578
896
802816
719323136
29.9333
9.6406 j
847
717-^09
607645423
29.1033
9-4615
897
804609
721734273
29.9500
9-6442 j
848
719104
609800192
29.1204
9.4652
898
806404
7.24150792
29.9666
9.64771
849
720801
61 1960049
29.1376
9.4690
890
808201
726572699
29-9833
9.65131
850
722500
614125000
29.1548
94727
•
900
810000
729000000
30.0000 9.6S49«
SQUARES, CUBES AND ROOTS
501
Squares, Cubes, Square and Cube Roots of Numbers from
I to I 000
No.
Square
Cube
Sq.
Root
Cube
Root
No.
Square
Cube
Sq.
Root
Cube
Root
901
811801
73 143 2 701
30.0167
9.6585
951
904401
860085351
30.8383
9.8339
902
813604
733870808
30.0333
9.6620
952
906304
862S01408
30.8545
9.8374
903
815409
736314327
30.0500
9.6656
953
908209
865523177
30.8707
9.8408
904
817216
738763264 30.0666
9.6692
954
910116
86S2 50664
30.8869
9.8443
905
819025
741217625130.0832
9.6727
955
912025
870983875
30.9031
9.8477
906
820836
743677416I30.0998
9.6763
956
913936
873722816
30.9192
9.8511
907
822649
746142643 130. 1 164
9.6799
957
915849
876467493
30.9354
9.8546
908
824464
748613312130.1330
9.6834
958
917764
879217912
30.9516
9.8580
909
826281
751089429I30.1496
9.6870
959
919681
^81974079
30.9677
9.8614
910
828100
753571000
30.1662
9.6905
960
921600
884736000
30.9839
9.8648
911
829921
756058031
30.1828
9.6941
961
923521
887503681
31.0000
9.8683
912
831744
758550528
30.1993
9.6976: 962
925444
890277128
31.0161
9.8717
913
833569
761048497
30.2159
9.7012 1 963
927369
893056347
31.0322
9.8751
914
835396
763551944
30.2324
9.7047 1 964
929296
895841344
31.0483
9.8785
915
837225
766060875
30.2490
9.7082: j 96s
931225
898632125
31.0644
9.8819
916
839056
768575296
30.2655
9.7118JI 966
933156
901428696
31.0805
9.8854
917
840889
771095213
30.2820
9.7153!; 967
935089
904231063
31.0966
9.8888
918
842724
773620632
30.2985
9.7188
968
937024 907039232
31.1127
9.8922
919
844561
776151559
30.3150
9.7224]
9.7259
969
938961! 909S53209
31.1288
9.8956
920
846400
778688000
30.3315
970
940900 1 912673000
31.1448
9.8990
921
848241
781229961
30.3480
9.7294I
971
942841 915498611
31.1609
9.9024
922
850084
7837774^8
30.3645
9.7329!! 972
944784' 918330048
31.1769
9.9058
923
851929
786330467
30.3809
9.7364 1 973
946729 921167317
31.1929
9.9092
924
853776
788889024
30.3974
9.7400 j 974
948676 924010424
31.2090
9.9126
925
855625
791453125
30.4138
9.7435' 975
950625
926859375
31.2250
9.9160
926
857476
794022776
30.4302
9.7470' 976
952576
929714176
31.2410
9.9194
927
859329
7965979S3
30.4467
9.7505' 977
954529
932574833
31.2570
9.9227
928
861184
799178752
30.4631
9.7540:
978
956484
935441352
31.2730
9.9261
929
863041
801765089
30.4795
9.7575!
979
958441
938313739
31.2890
9.9295
930
864900
804357000
30.4959
9.7610
980
960400
941192000
31.3050
9.9329
931
866761
806954491
30.5123
9.7645
981
962361
944076141
31.3209
9.9363
932
868624
809557568
30.5287
9.7680
982
964324
946966168
31.3369
9.9396
933
870489
812166237
30.5450
9.7715
983
966289
9498620S7
31.3528
9.9430
934
872356
814780504130.5614
9.7750 1 984
968256
952763904
31.3688
9.9464
935
874225
817400375 30.5778
9.7785'! 985
970225
955671625
31.3847
9.9497-
936
876096
820025856 30.5941
9.7819:1 986
972196
958585256
31.4006
9.9531
937
877969
822656953I30.6105
9.7854 987
974169
961504803
31.4166
9.9565
938
879844
825293672 30.6268
9.7889, 988
976144
964430272
31.4325
9.9598
939
881721
827936019130.6431
9.7924: 989
978121
967361669
31.4484
9.9632
940
883600
830584000
30.6594
9.7959
990
980100
970299000
31.4643
9.9666
941
885481
833237621
30.6757
9.79931
991
982081
973242271
31.4802
9.9699
942
887364
835896888
30.6920
9.8028
992
984064
976191488
31.4960
9.9733
943
889249
838561807
30.7083
9.8063 993
986049
979146657
31.5119
9.9766
944
891136
841232384
30.7246
9.8o97il 994
988036
982107784
31.5278
9.9800
945
893025
843908625 30.7409
9.8132 j 995
990025
985074875
31.5436
9.9833
946
894916
846590536
30.7571
9.8167 ! 996
992016
988047936
31.5595
9.9866
947
896809
849278123
30.7734
9.8201 ! 997
994009
991026973
31.5753
9.9900
948
898704
851971392
30.7896
9.8236 1 998
996004
994011992
31.5911
9.9933
949
900601
854670349
30.8058
9.82701 999
998001
997002999
31.6070
9.9967
950
902500
857375000
30.8221
9.8305 1000
I 000000
1000000000
31.6228
lO.OOOO
502
GENERAL REFERENCE TABLES
Areas and Circumferences of Circles from i to
100
Dia.
Area
Circum.
Dia.
Area
Circum.
Dia.
Area
Circum.
"S
0.00077
0.098175
2
3.1416
6.28319
5^
19-635
15.7080
■e\
0.00173
0.147262
tV
3-34IO
6.47953
tV
20.129
15.9043
tV
0.00307
0.196350
i
3-5466
6.67588
h
20.629
16.1007
3\
0.00690
0.294524
fV
3.7583
6.87223
A
21-135
16.2970
i
0.01227
0.392699
i
3.9761
7.06858
i
21.648
16.4934
A
O.OI917
0.490874
A
4.2000
7.26493
5
T6
22.166
16.6897
A
0.02761
0.589049
f
4.4301
7.46128
1
22.691
16.8861
3T
0.03758
0.687223
t\
4.6664
7.65763
A
23.221
17.0824
i
0.04909
0.785398
i
4.9087
7.85398
i
23-758
17.2788
3%
0.06213
0.883573
A
S-1572
8.05033
A
24.301
17.4751
A
0.07670
0.981748
1
5-4119
8.24668
f
24.850
17.6715
ii
0.09281
1.07992
ii
5.6727
8.44303
H
25.406
17.8678
f
O.I 1045
I.17810
f
5-9396
8.63938
f
25.967
18.0642
M
0.12962
1.27627
If
6.2126
8.83573
if
26.535
18.2605
1^
0.15033
1-37445
7
8
6.4918
9.03208
i
27.109
18.4569
M
0.17257
1.47262
if
6.7771
9.22843
if
27.688
18.6532
i
0.19635
1.57080
3
7.0686
9.42478
6
28.274
18.8496
H
0.22166
1.66897
tV
7.3662
9.62113
f
29.465
19.2423
T%
0.24850
1.76715
1
7.6699
9.81748
30.680
19.6350
if
0.27688
1.86532
A
7.9798
10.0138
f
31-919
20.0277
f
0.30680
1.96350
'i
8.2958
10.2102
i
33-183
20.4204
H
0.33824
2.06167
A
8.6179
10.4065
1
34.472
20.8131
16
0.37122
2.15984
i
8.9462
10.6029
3
i
35.785
21.2058
If
0.40574
2.25802
A
9.2806
10.7992
i
37.122
21.5984
f
0.44179
2.35619
1
9. 62 II
10.9956
7
38.485
21.9911
II
0.47937
2.45437
?
9.9678
11.1919
f
39.871
22.3838
tI
0.51849
2.55254
10.321
11.3883
41.282
22.7765
II
0.55914
2.65072
A
10.680
11.5846
f
42.718
23.1692
i
0.60132
2.74889
f
11.045
11.7810
i
44.179
23.5619
0.64504
2.84707
if
11.416
11.9773
f
45.664
23.9546
it
0.69029
2.94524
1
11-793
12.1737
f
47-173
24.3473
fi
0.73708
3-04342
if
12.177
12.3700
1
48.707
24.7400
I
0.78540
3-14159
4
12.566
12.5664
8
50.265
25.1327
'¥
0.88664
3-33794
iV
12.962
12.7627
i
51.849
25.5224
i
0.99402
3-53429
i
13-364
12.9591
i
53.456
25.9181
A
I.I075
3-73064
fV
13-772
13-1554
f
55-088
26.3108
i
1.2272
3.92699
i
14.186
13-3518
56.745
26.7035
t\
1-3530
4.12334
A
14.607
13-5481
f
58.426
27.0962
1
1 .4849
4.31969
f
15.033
13-7445
f
60.132
27.4889
1^
1.6230
4.51604
A
15.466
13.9408
I
61.862
27.8816
i
I.767I
4.71239
h
15.904
14.1372
9
63.617
28.2743
T%
1-9175
4.90874
i\
16.349
14.3335
1
65-397
28.6670
1
2.0739
5.10509
t
16.800
14.5299
4
67.201
29.0597
t*
2.2365
5-30144
ii
17-257
14.7262
i
69.C29
29.4524
f
2.4053
5-49779
3
4
17.721
14.9226
i
70.882
29.8451
^
2.5802
5.69414
H
18.190
15.I189
f
72.760
30.2378
i
2.7612
5.89049
i
18.665
15-3153
f
74.662
30.6305
H
2.9483
6.08684
if
19.147
15-5116
I
76.589
31.0232
AREAS AND CIRCUMFERENCES OF CIRCLES 503
Areas and Circumferences of Circles from i to
100
Dia.
Area
Circum.
Dia.
Area
Circum. '
Dia.
Area
Circum.
lO
78.540
31-4159
16
201.06
50.2655
22
380.13
69.1150
i
80.516
31.8086
1
204.22
50.6582
1
384.46
69.5077
.
82.516
32.2013
1
207.39
51.0509
388.82
69.9004
\
84.541
32.5940
1
210.60
51.4436
1
393.20
70.2931
86.590
32.9867
^
213.82
51.8363
h
397.61
70.6858
■ 1
88.664
33-3794
f
217.08
52.2290
f
402.04
71.0785
3
4
90.763
33-7721
1
220.35
52.6217
f
406.49
71.4712
I
92.886
34.1648
1
223.65
53.0144
i
410.97
71.8639
II
95-033
34.5575
17
226.98
53-4071
23^
415.48
72.2566
i
97.205
34.9502
i
230.33
53-7998
h
420.00
72.6493
i
99.402
35-3429
I
233-71
54.1925
i
424.56
73.0420
f
101.62
35.7356
f
237.10
54.5852
f
429.13
73-4347
1
103.87
36.1283
h
240.53
54.9779
1
433.74
73-8274
106.14
36.5210
1
243-98
55.3706
1
438.36
74.2201
f
108.43
36.9137
f
247-45
55-7633
f
443.01
74.6128
1
110.75
37-3064
i
250.95
56.1560
1
447.69
75-0055
12
113. 10
37.6991
18
254.47
56.5487
24
452.39
75-3982
f
11547
38.0918
i
258.02
56.9414
1
457.11
75-7909
117.86
38.4845
1
4
261.59
57-3341
i
461.86
76.1836
f
120.28
38.8772
f
26^.18
57.7268
f
466.64
76.5765
1
122.72
39.2699
1
268.80
58.1195
i
471.44
76.9690
f
125.19
39.6626
f
272.45
58.5122
f
476.26
77.3617
1
127.68
40.0553
f
276.12
58.9049
f
481. II
77-7544
i
130.19
40,4480
7
8
279.81
59.2976
I
485.98
78.1471
13
132.73
40.8407
19
283.53
59.6903
25
490.87
78.5398
1
135-30
41-2334
i
287.27
60.0830
1
495-79
78.9325
1
4
137.89
41.6261
1
4
291.04
60.4757
i
500.74
79.3252
f
140.50
42.0188
f
294.83
60.8684
1
505.71
79.7179
. h
143.14
42.4115
*
298.65
61.2611
i
510.71
80.1105
1
145.80
42.8042
1
302.49
61.6538
1
515.72
80.5033
f
148.49
43.1969
1
306.35
62.0465
f
520.77
80.8960
1
151.20
43-5896
1
310.24
62.4392
1
525.84
81.2887
14
153-94
43-9823
20
314.16
62.8319
26
530.93
81.6814
1
156.70
44.3750
i
318.10
63.2246
f
536.05
82,0741
159.48
44.7677
i
322.06
63.6173
541.19
82.4668
f
162.30
45.1604
i
326.05
64.0100
g
546.35
82.8595
1
165.13
45-5531
*
330.06
64.4026
551.55
83.2522
1
167.99
45-9458
1
334.10
64.7953
556.76
83.6449
f
170.87
46.3385
4
338.16
65.1880
¥
562.00
84.0376
1
173.78
46.7312
i
342.25
65.5807
1
567.27
84.4303
IS
176.71
47.1239
21
346.36
65-9734
27
572.56
84.8230
i
179.67
47-5166
1
350.50
66.3661
I 577.87
85.2157
^
182.65
47-9093
354.66
66.7588
583.21
85.6084
1
185.66
48.3020
1
358.84
67.1515
ii
588.57
86.0011
1
188.69
48.6947
1
363.05
67.5442 .
1
593-96
86.3938
1
191-75
49.0874
367.28
67.9369
1
599-37
86.7865
f
194.83
49.4801
1
371.54
68.3296
f
604.81
87.1792
1
197-93
49.8728
1
375.83
68.7223
i
610.27
87.5719
504
GENERAL REFERENCE TABLES
Areas and Circumferences of Circles from i to ioo
Dia
Area
Circum.
Dia
Area
Circum.
Dia
Area
Circum.
28
615.75
87.9646
34
907.92
106.814
40
1256.6
125.664
i
621.26
88.3573
1
914.61
107.207
i
1264.5
126.056
1
626.80
88.7500
I
921.32
107.600
J
1272.4
126.449
1
632.36
89.1427
i
928.06
. 107.992
\
1280.3
126.842
*
637-94
89-5354
\
934-82
108.385
\
1288.2
127.235
1
643-55
89.9281
f
941.61
108.788
1296.2
127.627,
t
649.18
90.3208
948.42
109.170
\
1304.2
128.020
7
8
656.84
90.7135
1
955-25
109.563
7
8
1312.2
128.413
29
660.52
91.1062
35
962. TI
109.956
41
1320.3
128.805
1
666.23
91.4989
\
969.00
110.348
1
1328.3
129.198
\
671.96
91.8916
\
975-91
II0.741
1
4
1336.4
129.591
1
677.71
92.2843
982.84
III. 134
1
1344.5
129.993
h
683.49
92.6770
1
989.80
III.527
h
1352.7
130.376
t
689.30
93.0697
1
996.78
1 1 1. 9 19
f
1360.8
130.769
:■
695-13
93.4624
f
1003.8
II2.312
f
1369.0
131. 161
700.98
93-8551
1
1010.8
112.705
7
1377.2
131.554
30
706.86
94.2478
2,(>
1017.9
113.097
42
1385.4
131-947
i
712.76
94.6405
\
1025.0
113.490
i
1393.7
132.340
1
718.69
95-0332
1
4
1032. 1
113.883
i
1402.0
132.732
i
724.64
95-4259
1
1039.2
114.275
§
1410.3
133.125
1
730.62
95.8186
\
1046.3
114.668
i
1418.6
133.518
f
736.62
96.2113
%
1053-5
I15.061
f
1427.0
133.910
f
742.64
96.6040
\
1060.7
115.454
f
1435.4
134.303
I
748.69
96.9967
I
1068.0
115.846
1
1443.8
134.696
3^
754-77
97-3894
31
1075.2
116.239
43
1452.2
135.088
i
760.87
97.7821
1
1082.5
116.632
1
1460.7
135.481
\
766.99
98.1748
i
1089.8
117.024
1
4
1469. 1
135.874
1
773-14
98.5675
1
1097.1
I17.417
1477.6
136.267
i
779-31
98.9602
i
1104.5
I17.810
1
1486.2
136.659
f
785-51
99.3529
1
1111.8
118.202
1494.7
137.05^
f
791-73
99.7456
1
1119.2
118.596
1
1503.3
137.445
1
797.98
100.138
I
1126.7
118.988
1
1511.9
137.837
32
804.25
100.531
38
1134.1
I19.381
44
1520.5
138.230
i
810.54
100.924
f
1141.6
119-773
\
1529.2
138.623
i
816.86
101.316
1149.1
120.166
1537.9
139.01.5
1
823.21
101.709
1
1 156.6
120.559
1
1546.6
139.408
i
829.58
102.102
1
II 64.2
120.951
*
1555-3
139.801
f
835-97
102.494
f
1171.7
121.344
f
1564.0
140.194
f
842.39
102.887
1179.3
121.737
\-
1572.8
140.586
7
8
848.83
103.280
1
1 186.9
122.129
l
1581.6
140.979
33
855.30
103.673
39
1 194.6
122.522
45,
1590.4
141.372
I
861.79
104.065
f
1202.3
122.915
f
1599.3
141.764
i
868.31
104.458
1210.0
123.308
1608.2
142.157
1
874.85
104.851
1
1217.7
123.700
^'•-
1617.0
142.550
^
881.41
105.243
h
1225.4
124.093
h
1626.0
142.942
f
888.00
105.636
1
1233.2
124.486
1
1634.9
T-^3-Z3S
f
894.62
106.029
1241.0
124.878
1643.9
143.728
1 901.26 1
106.421
I
1248.8
125.271
1652.9 1 144. 121
AREAS AND CIRCUMFERENCES OF CIRCLES 505
Areas and Circumferences
DF Circles from i tc
) 100
Dia.
Area
Circum.
Dia.
Area
Circum.
Dia.
Area
Circum.
46
1661.9
144.513
52
2123.7
163.363
S8
2642.1
182.212
f
1670.9
144.906
i
2133-9
163.756
^ i
2653-5
182.605
1680.0
145.299
i
2144.2
164.148
i
2664.9
182.998
f
1689. 1
145.691
f
2154.5
164.541
1
2676.4
183.390
1
1698.2
146.084
1
2164.8
164.934
1
2687.8
^^3-783
. f
1707.4
146.477
2175. I
165.326
2699.3
184.176
f
1 7 1.6.5
146.869
f
2185.4
165.719
J
2710.9
184.569
i
1725-7
147.262
i
2195.8
166. 112
i
2722.4
184.961
47
1734-9
^47-655
53
2206.2
166.504
59
2734.0
185.354
i
1744.2
148.048
i
2216.6
166.897
i
2745-6
185.747
i
1753-5
148.440
i
2227.0
167.290
i
2757-2
186.139
§
1762.7
148.833
1
2237-5
167.683
1
2768.8
186.532
f
1772. I
149.226
1
2248.0
168.075
h
2780.5
186.925
1781.4
149.618
2258.5
168.468
1
2792.2
187.317
f
1790.8
150.011
f
2269.1
168.861
T
2803.9
187.710
i
1800. 1
150.404
1
2279.6
169.253
1
2815.7
188.103
48
1809.6
150.796
54
2290.2
169.646
60
2827.4
188.496
f
1819.0
151. 189
f
2300.8
170.039
i-
2839.2
188.888
1828.5
151.582
2311-5
170.431
1
2851.0
189.281
1
18379
151-975
1
2322.1
170.824
f
2862.9
189.674
*
1847-5
152-367
1
2332.8
171.217
i
2874.8
190.066
f
1857.0
152.760
2343.5
171.609
f
2886.6
190.459
f
1866.5
153-153
f
2354.3
172.002
f
2898.6
190.852
1
1876.1
153.544
1
2365.0
172.395
1
2910.5
191.244
49,
1885.7
153.938
55
2375.8
172.788
61
2922,5
191.637
I
1895.4
154-331
1
2386.6
173.180
i
2934.5
192.030
1
4
1905.0
154-723
I
2397.5
173-573
I
2946.5
192.423
f
1914.7
155-I16
f
2408.3
173.966
1
2958.5
192.815
i
1924.2
155-509
h
2419.2
174-358
i
2970.6
193.208
1
1934.2
155-904
f
2430.1
174.751
f
2982.7
193.601
f
1943.9
156.294
f
2441. 1
175-144
3
4
2994.8
193-993
1
1953-7
156.687
i
2452.0
175-536
i
3006.9
194.386
5°,
1963.5
157.080
56
2463.0
175.929
62
3019.1
194.779
i
1973-3
157.472
1
2474.0
176.322
i
3031-3
195. 171
i
1983.2
157.865
i
2485.0
176.715
1
4
3043-5
195-564
i
1993.1
158.258
f
2496.1
177.107
1
3055-7
195-957
i
2003.0
158.650
2507.2
177.500
h
3068.0
196.350
f
2012.9
159.043
1
2518.3
177.893
f
3080.3
196.742
f
2022.8
159.436
f
2529.4
178.285
f
3092.6
197.135
i
2032.8
159.829
i
2540.6
178.678
1
3104.9
197.528
51
2042.8
160.221
57
2551.8
179.071
63
3117.2
197.920
1
2052.8
160.614
i
2563.0
179.463
f
3129.6
198.313
i
2062.9
161.007
i
2574.2
179.856
31.42.0
198.706
i
2073.0
161.399
1
2585.4
180.249
1
3154.5
199.098
i
2083. T
161.792
h
2596.7
180.642
^
3166.9
199.491
1
2093.2
162.185
1
2608.0
181.034
1
3^79-4
199.884
4
2103.3
162.577
1
2619.4
181.427
1
3191-9
200.277
1
2II3.5
162.970
2630.7
181.820
1 3204.4 1
200.669
5o6.
GENERAL REFERENCE TABLES
Areas and Circumferences
OF Circles from i to 100
Dia.
Area
Circum.
pia.
Area
Circum.
Dia.| Area
Oircum.
64
3217.0
201.062
70
3848.5
219.911
76
4536.5
238.761
1
3229.6
201.455
1
3862.2
220.304
i
4551.4
239.154
i
3242.2
201.847
i
3876.0
220.697
\
4566.4
239-546
f
3254.8
202.240
1
3889.8
221.090
1
4581.3
239-939
i
3267.5
202.633
i
3903.6
221.482
\
4596.3
240332
f
3280.1
203.025
f
3917-5
221.875
f
461 1. 4
240.725
f
3292.8
203.418
f
3931-4
222.268
¥
4626.4
241.117
1
3305.6
203.811
i
3945-3
222.660
1
4641.5
■241.510
65
3318.3
204.204
71
3959-2
223.053
77
4656.6
241.903
i
333^--^
204.596
i
3973-1
223.446
\
4671.8
242.295
i
3343.9
204.989
i
3987-1
223.838
\
4686.9
242.688
f
3356.7
205.382'
1
4001. 1
224.231
I
4702.1
243.081
1
3369.6
205.774
i
4015.2
224.624
\
4717.3
243-473
3382.4
206.167
1
4029.2
225.017
4732.5
243-866
1
3395-3
206.560
f
4043-3
225.409
\
4747.8
244.259
1
3408.2
206.952
i
4057-4
225.802
\
4763.1
244.652
66
3421.2,
207.345
72
4071.5
226.195
78
4778.4
245.044
i
3434.3
207.738
i
4085.7
226.587
\
4793.7
245-437
i
3447-2
208.131
\
4099.8
226.930
\
4809.0
245-830
•1
3460.2
208.523
1
4114.0
227.373
4824.4
246.222
^
3473-2
208.916
\
4128.2
227.765
1
4839.8
246.615
f
3486.3
209.309
1
4142.5
228.158
1
4855.2
247.008
f
3499-4
209.701
3.
4
4156.8
228.551
f
4870.7
247.400
1
3512.5
210.094
I
4171.1
228.944
I
4886.2
247.793
67
3525-7
210.487
73
4185.4
229.336
79
4901.7
248.186
1
3538-8
210.879
i
4199.7
229.729
\
4917.2
248.579
^
3552.0
211.272
i
4214.1
230.122
\
4932.7
248.971
f
3565.2
211.665
f
4228.5
230.514
\
4948.3
249-364
1
3578.5
212.058
i
4242.9
230.907
\
4963.9
249-757
f
3591.7
212.450
f
4257.4
231.300
8
4979.5
250.149
f
3605.0
212.843
f
4271.8
231.692
4
4995.2
250.542
i
3618.3
213.236
i
4286.3
232.085
i
5010.9
250.935
68
3631.7
213.628
74
4300.8
232.478
80
5026.5
251.327
1
3645.0
214.021
i-
4315.4
232.871
\
5042.3
251.720
i
3658.4
214.414
i
4329.9
233.263
5058.0
252.113
1
3671.8
214.806
1
4344.5
233-656
8
5073.8
252.506
h
3685.3
215.199
\
4359.2
234.049
\
5089.6
252.898
f
3698.7
215.592
f
4373-8
234.441
' f
5105.4
253.291
f
3712.2
215-984
f
4388.5
234-334
f
512I.2
253-684
1
3725-7
216.337
i
4403.1
235.227
I
5137-1
254.076
69
3739.3
216.770
75
4417-9
235.619
81
5153-0
254.469
i
3752.8
217.163
\
4432-6
236.012
\
5168.9
254.862
1
4
3766.4
217-555
4447-4
236.405
5184.9
255-254
1
3780.0
217.948
1
4462.2
236.798
1
5200.8
255-647
^
3793.7
218.341
\
4477.0
237.190
\
5216.8
256.040
f
3807.3
218.733
f
4491.8 >
237.583
1
5232.8
256.433
f
3821.0
219.126
4506.7
237.976
1
5248.9
256.825
i
3834.7
219.519
i
4521.5
238.368
1
5264.9
257.218
AREAS AND CIRCUMFERENCES OF CIRCLES 5^7
Areas and Circumferences (
DF Circles from i to
100
Dia.
Area
Circum.
JDia.
^ Area
Circum.
Dia.
Area
Circtim.
87
5281.0
257.611
88
6082.1
276.460
94
6939.8
295.310
i
5297-1
258.003
i
6099.4
276.853
i
6958.2
295-702
i
5313-3
258.396
\
6256.7
277.846
1
4
6976.7
296.095
1
5329-4
258.789
i
6134-1
277.638
1
6995-3
296.488
5345-6
259.181
i
6151.4
278.031
h
7013.8
296.881
1
5361.8
259.574
1
6168.8
278.424
1
7032.4
297.273
1
5378.1
259-967
f
6186.2
278.816
7051.0
297.666
1
5394-3
260.359
I
6203.7
279.209
s
7069.6
298.059
83
5410.6
260.752
89
6221. I
279.602
95
7088.2
298.451
'*
5426.9
261.145
i
6238.6
279.994
1
7106.9
298.844
i
5443-3
261.538
1
4
6256.1
280.387
\
7125.6
299.237
f
5459-6
261.930
i
6273-7
280.780
f
7144.3
299.629
^
5476.0
262.323
h
6291.2
281.173
\
7163.0
300.022
1
5492.4
262.716
f
6308.8
281.565
i
7181.8
300.415
i
5508.8
263.103
6326.4
281.958
f
7200.6
300.807
1
5525-3
263.501
1
6344.1
282.351
1
7219.4
301.200
84
5541.8
263.894
90
6361.7
282.743
96
7238.2
301.593
i
5558.3
264.286
1
6379-4
283.136
i
7257-1
301.986
:■
5574.8
264.679
1
6397.1
283.529
\
7276.0
302.378
5591.4
265.072
1
6414.9
283.921
1
7294.9
302.771
1
5607.9
265.465
*
6432.6
284.314
h
7313-8
303.164
f
5624.5
265.857
f
6450.4
284.707
i
7332.8
303-556
f
5641.2
266.250
f
6468.2
285.100
2.
4
7351.8
303-949
i
5657-8
266.643
I
6486.0
285.492
I
7370.8
304.342
^5,
5674-5
267.035
91
6503.9
285.88s
97
7389.8
304.734
i
5691.2
267.428
1
6521.8
286.278
i
7408.9
305.127
i
5707-9
267.821
i
6539-7
286.670
\
7428.0
305.520
1
5724-7
268.213
f
6557-6
287.063
f
7447-1
305.913
^
5741.5
268.606
\
6575-5
287.4S6
i
7466.2
306.305
f
5758.3
268.999
f
6593-5
287.848
f
7485-3
306.698
f
5775.1
269.392
661 1.5
288.241
1
7504.5
307.091
i
5791.9
269.784
I
6629.6
288.634
1
7523-7
307-483
86
5808.8
270.177
92
6647.6
289.027
98
7543-0
307.876
i
5825.7
270.570
i
6665.7
289.419
1
7562.2
308.269
i
5842.6
270.962
I
6683.8
289.812
I
7581.5
308.661
1
5859-6
271.355
i
6701.9
290.205
i
7600.8
309-064
h
5876.5
271.748
i
6720.1
290.597
i
7620.1
309-447
f
5893.5
272.140
1
6738.2
290.990
1
7639.5
309.840
f
5910.6
272.533
1
6756.4
291.383
1
7658.9
310.232
i
5927-6
272.926
1
6774.7
291.775
i
7678.3
310.625
^h
5944-7
273-319
93
6792.9
292.168
99^
7697-7
311.018
i
5961.8
273.711
\
6811.2
292.561
i
7717.1
311.410
i
5978.9
274.104
6829.5
292.954
i
7736.6
311.803
1
5996.0
274-497
1
6847.8
293-346
1
7756.1
312.196
1
6013.2
274.889
\
6866.1
293-739
J
7775.6
312.588
1
6030.4
275.282
f
6884.5
294.132
f
7795-2
312.981
6047.6
275-675
6902.9
294.524
f
7814.8
313-374
1 6064.0
276.067
6921.3
294.917
i
7834.4
313.767
5o8 GENERAL REFERENCE TABLES
Areas and Circumferences of. Circles from ioo to iooo
Diam.
Area.
Circum.
Diam.
Area
Circum.
Diam.
Area
Circum.
lOO
7853-98
314-16
150
17671.46
471.24
200
31415-93
628.32
lOI
8011.85
317-30
151
17907.86
474-38
201
31730.87
631.46
I02
8171.28
320.44
152
18145.84
477-52
202
32047-39
634.60
103
8332-29
323-58
153
18385.39
480.66
203
32365.47
^.^''■li
104
8494.87
326.73
154
18626.50
483-81
204
32685.13
640.88
los
8659.01
329-87
155
18869,19
486.95
20S
33006.36
644-03
106
8824.73
333-01
156
191 13.45
490.09
206
33329-16
647-17
107
8992.02
336.15
157
19359.28
493-23
207
33653-53
650.31
108
9160.88
339-29
158
19606.68
496.37 .
208
33979-47
653-45
109
9331-32
342.43
159
19855.65
499.51
209
34306.98
65659
no
9503-32
345-58
160
20106.19
502.6s
210
34636.06
659-73
III
9676.89
348.72
161
20358.31
505.80
211
34966.71
662.88
112
9852-03
351-86
162
20611.99
508.94
212
35298.94
666.02
113
10028.7s
355-00
163
20867.24
512.08
213
35632.73
669.16
114
10207.03
358.14
164
21124.07
515.22
214
35968.09
672.30
115
10386.89
361.28
i6s
21382.46
S18.36
215
36305.03
^75-44
116
10568.32
364-42
166
21642.43
521.50
216
36643.54
678.58
117
10751.32
367-57
167
21903.97
524.65
217
36983.61
681.73
118
I093S-88
370.71
■ 168
22167.08
527.79
218
37325.26
684.87
119
11122.02
373-85
£69
22431.76
530.93
219
37668.48
688.01
120
11309.73
376.99
170
22698.01
534.07
220
38013.27
691.15
121
I 1499.01
380.13
171
22965.83
537-21
221
38359.63
694.29
122
11689-87
383.27
172
23235.22
540.35
222
38707-56
697-43
123
11882.29
386.42
173
23506.18
543.50
2.23
39057.07
700.58
124
12076.28
389.56
174
23778.71
546.64
224
39408.14
703.72
125
12271.85
392.70
175
24052.82
549.78
225
39760.78
706.86
126
12468.98
395.84
176
24328.49
552.92
226
40115.00
710.00
127
12667.69
398.98
177
24605.74
556.06
227
40470.78
713.14
128
12867.96
402.12
178
24884.56
5.59.20
228
40828:14
716.28
129
13069.81
405-27
179
25164.94
562.35
229
41187-07
719.42
130
13273-23
408.41
180
25446.90
565.49
230
41547-56
722.57
131
13478-22
411-55
181
25730.43
568.63
231
41909.63
725.71
132
13684.78
414.69
182
26015.53
571-77
232
42273.27
728.8s
133
13892.91
417.83
183
26302.20
574.91
233
42638.48
731.99
134
14102.61
420.97
184
26590.44
578.0s
234
43005.26
735.13
135
14313-88
424.12
185
26880.25
581.19
235
43373.61
738.27
136
14526.72
427.26
186
27171.63
584.34
236
43743-54
741.42
137
14741.14
430.40
187
27464.59
587.48
237
44115-03
744.56
138
14957-12
433-54
188
27759-11
590.62
238
44488.09
747.70
139
15174-68
436.68
1S9
28055-21
593.76
239
44862.73
750.84
140
15393-80
439-82
190
28352-87
596.90
240
45238.93
753.98
141
15614.50
442.96
191
28652.11
600.04
241
45616.71
757.12
142
15836.77
446.11
192
28952.92
603.19
242
45996.06
760.27
143
16060. 6i
449.25
193
29255-30
606.33
243
46376.98
763.41
144
16286.02
452.39
194
29559-25
609.47
244
46759-47
766.5s
14s
16513.00
455-53
195
29864-77
612.61
245
47143-52
769.69
146
16741-55
458.67
196
30171-86
61S.75
246
47529.16
772.83
^47
16971.67
461.81
197
30480.52
618.89
247
47916.36
775.97
148
17203.36
464.96
198
30790.75
622.04
248
48305.13
779.11
149
17436.62
468.10
199
31102.55
625.18
249
48695.47
782.26
AREAS AND CIRCUMFERENCES 509
Areas and Circumferences of Circles from 100 to iooo
Diam.
Area
Circum.
Diam.
Area
Circum.
Diam.
Area
Circum.
250
49087.39
785.40
300
7.0685.83
942.48
350
96211.28
1099.56
251
49480.87
788.54
301
71157.86
945.62
351
96761.84
1102.70
252
49875.92
791.68
302
71631.45
948.76
352
97313.97
1105.84
253
50272.55
794.82
303
72106.62
951-90
353
97867.68
1108.98
254
50670.75
797.96
304
72583.36
955-04
354
98422.96
1112.12
25s
51070.52
801. II
30s
73061.66
958.19
355
98979-80
1115.27
256
51471.85
804.25
306
73541-54
961.33
356
99538.22
1118.41
257
51874.76
807.39
307
74022.99
964.47
357
100098.21
1121.55
258
52279.24
810.53
308
74506.01
967.61
358
100659.77
1124.69
25Q
52685.29
813.67
309
74990.60
970.75
359
101222.90
1127.83
260
53092.92
816.81
310
75476.76
973.89
360
101787.60
1130.97
261
53502.11
819.96
311
75964.50
977.04
361
102353.87
1134-11
262
53912.87
823.10
312
76453.80
980.18
362
102921.72
1137-26
263
54325.21
826.24
313
76944.67
983.32
363
103491-13
1140.40
264
54739-11
829.38
314
77437-12
986.46
364
104062.12
1143.54
265
55154.59
832.52
315
77931.13
989.60
365
104634.67
1146.68
266
55571.63
835.66
316
78426.72
992.74
366
105208.80
1149.82
267
55990.25
838.81
317
78923.88
995.88
367
105784.49
1152.96
268
56410.44
841.95
318
79422.60
999.03
368
106361.76
1156.11
269
56832.20
845-09
319
79922.90
1002.17
369
106940.60
1159-25
270
57255.53
848.23
320
80424.77
1005.31
370
107521.01
1162.39
271
57680.43
851-37
321
80928.21
1008.45
371
108102.99
1165.53
272
58106.90
854-51
322
81433.22
1011.59
372
108686.54
1168.67
273
58534.94
857-65
323
81939.80
1014.73
373
109271.66
1171.81
274
58964.55
860.80
324
82447.96
1017.88
374
109858.35
1174.96
275
59395-74
863.94
325
82957.68
1021.02
375
110446.62
1178.10
276
59828.49
867.08
326
83468.98
1024.16
376
I I 1036.45
1181.24
277
60262.82
870.22
327
83981.84
1027.30
377
111627.86
1184.38
278
60698.71! 873.36
328
84496.28
1030.44
378
112220.83
1187.52
279
61136.18
876.50
329
85012.28
1033.58
379
112815.38
1190.66
280
61575-22
879.65
330
85529.86
1036.73
380
113411.49
1193.81
281
62015.82
882.79
331
86049.01
1039.87
381
1 14009. 18
1196.9s
282
62458.00
885.93
332
86569.73
1043.01
382
114608.44
1200.09
283
62901.75
889.07
333
87092.02
1046.15
383
115209.27
1203.23
284
63347.07
892.21
334
87615.88
1049.29
384
115811.67
1206.37
285
63793-97
895.35
335
88141.31
1052.43
385
116415.64
1209.51
286
64242.43
898.50
336
88668.31
1055-58
386
117021.18
1212.65
287
64692.46
901.64
337
89196.88
1058.72
387
117628.30
1215.80
288
65144.07
904.78
338
89727.03
1061.86
388
118236.98
1218.94
289
65597.24
907.92
339
90258.74
1065.00
389
118847.24
1222.08
290
66051.99
911.06
340
90792.03
1068.14
390
119459.06
1225.22
2QI
66508.30
914.20
341
91326.88
1071.28
391
120072.46
1228.36
292
66966.19
917.35
342
91863.31
1074.42
392
120687.42
1231.50
293
67425.65
920.49
343
92401.31
1077.57
393
121303.96
1234-65
294
67886.68
923.63
344
92940.88
1080.71
394
12x922.07
1237-79
295
68349.28
926.77
345
93482.02
1083.85
395
122541-75
1240.93
296
68813.45
929.91
346
94024.73
1086.99
396
123163.00
1244.07
297
69279-19
933.05
347
94569.01
1090.13
397
123785.82
1247. 2.1
298
69746.50
936.19
348
95114.86
1093.27
398
124410.21
1250.3s
299
70215.38
939-34
349
95662.28
1096.42
399
125036.17
1253-50
510 GENERAL REFERENCE TABLES
Areas and Circumferences of Circles from ioo to iooo
Diam.
Area
Circum.
Diam.
Area
Circum.
Diam.
Area
Circm.
400
125663.71
1256.64
450
159043-13
^'^^Hi
500
196349.54
1570.80
401
126292.81
1259-78
451
159750.77
1416.86
SOI
197135-72
1573.94
402
126923.48
1262.92
452
160459.99
1420.00
502
197923-48
1577.08
403
127555-73
1266.06
453
161170.77
1423.14
503
198712.80
1580.22
404
128189.55
1269.20
454
161883.13
1426.28
504
199503-70
1583.36
40s
128824.93
1272.35
455
162597.05
1429.42
505
200296.17
1586.50
406
129.^61.89
1275.49
456
163312.55
1432.57
506
201090.20
1589.65
407
130100.42
1278.63
457
164029.62
1435.71
-507
201885.81
1592.79
408
130740.52
1281.77
458
164748.26
1438.85
508
202682.99
1595-93
409
131382.19
1284.91
459
165468.47
1441.99
509
203481.74
1599.07
410
132025.43
1288.0S
460
166190.25
1445.13
510
204282.06
1602.21
411
132670.24
1291.19
461
166913.60
1448.27
511
205083.95
1605.35
412
133316.63
1294-34
462
167638.53
1451.42
512
205887.42
1608.50
413
133964.58
1297.48
463
168365.02
1454-56
513
206692.45
1611.64
414
134614.10
1300.62
464
169093.08
1457-70
514
207499.05
1614.78
415
135265.20
1303.76
465
169822.72
1460.84
515
208307.23
1617.92
416
135917.86
1306.90
466
170553.92
1463-98
516
209116.97
1621.06
417
136572.10
1310.04
467
171286.70
1467-12
517
209928.29
1624.20
418
137227.91
1313.19
468
172021.05
1470.27
518
210741.18
1627.34
419
137885.29
1316.33
469
172756.97
1473.41
519
211555.63
1630.49
420
138544.24
1319-47
470
173494.45
1476.55
520
212371.66
1633.63
421
139204.76
1322.61
471
174233.51
1479.69
521
213189.26
1636.77
422
139866.85
1325-75
472
174974.14
1482.83
522
214008.43
1639.91
423
140530.51
1328.89
473
175716.35
1485.97
523
214829.17
1643.05
424
141195-74
1332.04
474
176460.12
1489.11
524
215651.49
1646.19
425
141862.54
1335-18
475
177205.46
1492.26
^^1
216475.37
1649.34
426
142530.92
1338-32
476
177952.37
1495.40
526
217300.82
1652.48
427
143200.86
1341-46
477
178700.86
1498.54
527
218127.85
1655.62
428
143872.38
1344.60
478
179450.91
1501.68
528
218956.44
1658.76
429
144545-46
1347-74
479
180202.54
1504.82
529
219786.61
1661.90
430
145220.12
1350.88
480
180955.74
1507.96
530
220618.34
1665.04
431
145896.35
1354-03
481
181710.50
1511.11
531
221451.65
1668.19
432
146574-15
1357-17
482
182466.84
1514-25
532
222286.53
1671.33
433
147253.52
1360.31
483
183224.75
1517.39
533-
223122.98
1674.47
434
147934-46
1363-45
484
183984.23
1520.53
534
223961.00
1677.61
435
148616.97
1366.59
485
184745.28
1523.67
535
224800.59
1680.75
436
149301.05
1369-73
486
185507.90
1526.81
536
225641.75
1883.89
437
149986.70
1372-88
487
186272.10
1529.96
537
226484.48
1687.04
438
150673.93
1376.02
488
187037.86
1533.10
538
227328.79
1690.18
439
151362.72
1379.16
489
187805.19
1536.24
539
228174.66
1693.32
440
152053.08
1382.30
490
188574.10
1539.38
S40
229022.10
•1696.46
441
152745.02
1385.44
491
189344.57
1542.52
541
229871.12
1699.60
442
153438.53
1388.58
492
190116.62
1545-66
542
230721.71
1702.74
443
154133-60
1391-73
493
190890.24
1548.81
543
231573.86
1705.88
444
154830.25
1394-87
494
191665.43
1551.95
544
232427.59
1709.03
445
155528.47
1398.01
495
192442.18
1555.09
545
233282.89
1712.17
446
156228.26
1401.15
496
193220.51
1558-23
546
234139.76
1715.31
447
156929.62
1404.29
497
194000.41
1561.37
547
234998.20
1718.4s
448
157632.55
1407-43
498
194781.89
1564-51
548
235858.21
1721.59
449
158337-06
1410.58
499
195564.93
1567-65
549
236719.79
1724-73
AREAS AND CIRCUMFERENCES 511
Areas and Circumferences of Circles from 100 to iooo
Diam.
Area
Circum.
Diam.
Area
Circum.
Diam.
Area
Circum.
550
237582.94
1727.88
600
282743.34' 1884.96
650
331830.72
2042.04
551
238447.67
1731.02
60 1
2836S6.60; 1888.10
651
332852.53
2045.18
552
239313-96
1734-16
602
284631.44' 1891.24
652
333875-90
2048.32
553
240181.83
1737-30
603
285577.84, 1894.38
653
334900.85
2051.46
554
241051.26
1740.44
604
286525.82! 1897.52
654
335927-36
2054.60
555
241922.27
1743.58
605
287475.361 1900.66
655
336955.45
2057.74
5S6
242794-85
1746-73
606
288426.48: 1903.81
656
337985.10
2060.88
557
243668.99
1749.87
607
289379.17
1906.95
^57
339016.33
^2064. 03
558
244544.71
1753.01
608
290333.43
1910.09
658
340049.13
2067.17
55Q
245422.00
1756.15
609
291289.26
1913.23
659
341083.50
2070.31
560
246300.86
1759.29
610
292246.66
1916.37
660
342119-44
2073.4s
561
247181.30
1762.43
6n
293205.63 1919.51
661
343156.95
2076.59
562
248063.30
1765.58
612
294166. 17I 1922.65
662
344196.03
2079.73
563
248946.87
1768.72
613
295128.28; 1925.80
663
345236.69
2082.88
564
249832.01
1771.86
614
296091.971 1928.94
664
346278.91
2086.02
565
250718.73
1775.00
615
297057.22 1932.08
665
347322.70
2089.16
566
251607.01
1778.14
616
298024.05! 1935-22
666
348368.07
2092.30
567
252496.87
1781.28
617
298992.44 1938.36
667
34941 S-00
2095.44
568
253388.30
1784.42
618
299962.41 1941-50
668
350463-51
2098.58
569
254281.29
1787.57
619
300933-95, 1944-65
669
351513.59
2101.73
570
255175-86
1790.71
620
301907.05' 1947-79
670
352565.24
2104.87
571
256072.00
1793-85
621
302881.73 1950.93
671
353618.45
2108.01
572
256969.71
1796.99
622
303857.98 1954-07
672
354673-24
2111.1S
573
257868.99
1800.13
623
304835.80
19^7.21
673
355729-60
2114.29
574
258769-85
1803.27
624
305815.20
1960.35
674
356787.54
2117.43
575
259672.27
1806.42
625
306796.16
1963-50
675
357847-04
2120.58
576
260576.26
1809.56
626
307778.69
1966.64
676
358908.11
2123.72
577
261481.83
1812.70
627
308762.79
1969.78
677
359970.75
2126.86
578
262388.96
1815.84
628
309748.47
1972.92
678
361034.97
2130.00
579
263297.67
1818.98
629
310735-71
1976.06
679
362100.75
2133-14
580
264207.94
1822.12
630
311724.53
1979-20
680
363168.11
2136.28
581
265119-79
1825.27
631
312714.92
1982.35
681
364237.04
2139.42
582
266033.21
1828.41
632
313706.88
1985.49
682
365307.54
2142.57
583
266948.20
1831.55
633
314700.40
1988.63
683
366379.60
2145.71
584
267864.76
1834.69
634
315695.50
1991-77
684
367453.24
2148.8s
585
2687S2.89
1S37.83
635
316692.17
1994.91
685
368528.45
2151.99
586
269702.59
1840.97
636
317690.42
1998.05
686
369605.23
2155.13
587
270623.86
1844.11
637
318690.23
2001.19
687
370683.59
2158.27
588
271546.70
1847.26
638
319691.61
2004.34
688
371763.51
2161.42
589
272471-12
1850.40
639
320694.56
2007.48
689
372845.00
2164.56
590
273397.10
1853.54
640
321699.09
2010.62
600
373028.07
2167.70
591
274324.66
1856.68
641
322705.18
2013.76
691
375012.70
2170.84
592
275253-78
1859.82
642
323712.85
2016.90
692
376098.91
2173-98
593
276184.48
1862.96
643
324722.09
2020.04
693
377186.68
2177-12
594
277116.75
1866.11
644
325732.89
2023.19
694
378276.03
2180.27
595
278050.58
1869.25
645
326745.27
2026.33
695
379366.93
2183.41
596
278985.99
1872.39
646
327759.22
2029.47
696
380459 44
2186.55
597
279922.97
1875.53
647
328774.74
2032.61
697
381553.50
2189.69
598
280861.52
1878.67
648
329791.83
2035-75
698
382649.13
2192.83
599
281801.65
1881.81
649
330810.49
2038.89
699
383746.33
2195.97
512 GENERAL REFERENCE TABLES
Areas and Circumferences of Circles from ioo to iooo
Area
384845.10
385945.44
387047.36
388150.84
380255-90
390362.52
391470.72
392580.4Q
393691.82
394804.73
395919.21
397035-26
398152.89
399272.08
400392.84
401515.18
402639.08
403764.56
404891.60
406020.22
407150.41
408282.17
409415.50
410550.40
411686.87
412824.91
413964.52
415105.71
416248.46
417392.79
418538.68
419686.15
420835.19
421985.79
423137-97
424291-72
425447-04
426603.94
427762.40
428922.43
430084.03
431247.21
432411.9s
433578.27
434746-16
435915-62
437086.64
438259.24
439433-41
440609.16
Circum.
Diam.
2199.11
750
2202.26
751
2205.40
752
2208.54
753
2211.68
754
2214.82
755
2217.96
756
2221. II
757
2224.25
7.58
2227.39
759
2230.53
760
2233.67
761
2236.81
762
2239-96
763
2243.10
764
2246.24
765
2249.38
766
2252.52
767
2255.66
768
2258.81
769
2261.95
770
2265.09
771
2268.23
772
2271.37
773
2274-51
774
2277-65
775
2280.80
776
2283.94
777
2287.08
778
2290.22
779
2293-36
780
2296.50
781
2299-65
782
2302.79
783
2305-93
784
2309.07
785
2312.21
786
2315-35
787
2318.50
788
2321.64-
789
2324.78
790
2327.92
791
2331.06
792
2334-20
793
2337-34
794
2340-49
795
2343-63
796
2346-77
797
2349-91
798
2353-05
799
Area
441786.47
442965-35
444145.80
445327-83
446511.42
447696-59
448883-32
450071.63
451261.51
452452.96
453645-98
454840.57
456036.73
457234-46
458433-77
459634-64
460837.08
462041.10
463246.69
464453.84
465662.57
466872.87
468084.74
469298.18
470513.19
471729-77
472947-92
474167-65
475388.94
476611.81
477836.24
479062.25
480289.83
481518.97
48274969
483981.98
485215-84
486451.28
487688.28
488926.85
490166.99
491408.71
492651.99
493896.85
495143-28
496391-27
497640.84
498891.98
500144.69
501398.97
Circum.
Diam.
2356.19
800
2359-34
801
2362.48
802
2365.62
803
2368.76
804
2371-90
805
2375 04
806
2378.19
807
2381.33
808
2384.47
809
2387.61
810
2390.75
811
2393-89
812
2397-04
813
2400.18
814
2403.32
815
2406.46
8x6
2409.60
817
2412.74
8x8
2415-88
819
2419-03
820
2422.17
821
2425-31
822
2428.45
823
2431-59
824
2434-73
825
2437-88
826
2441.02
827
2444.16
828
2447.30
829
2450.44
830
2453-58
831
2456.73
832
2459-87
833
2463.01
834
2466.15
835
2469-29
836
2472.43
837
2475-58
838
2478.72
839
2481.86
840
2485.00
841
2488.14
842
2491.28
843
2494-42
844
2497-57
845
2500.71
846
2503-85
847
2506.99
848
2510.13
849
Area
502654.82
503912.25
505171-24
506431.80
507693-94
508957-64
510222.92
511489-77
512758.19
514028.18
515299-74
516572.87
517847.57
519123.84
520401.68
521681.10
522962.08
524244.63
525528.76
526814.46
528101.73
529390.56
530680.97
53i972;95
533266.50
53456X.62
535858.32
537156.58
538456.41
539757-82
541060.79
542365.34
543671-46
544979-15
546288.40
547599-23
548911.63
550225.61
551541-15
552858.26
554176.94
S55497-20
556819.02
558x42.42
559467-39
560793-92
562122.03
563451-71
564782.96
566115.78
Circum.
AREAS AND CIRCUMFERENCES 513
Areas and Circumferences of Circles from 100 to iooo
Diam.
Area
Circum.
Diam.
Area
Circum.
Diam.
Area
Circum.
850
567450.17
2670.35
900
636172.51
2827.43
950
708821.84
2984-51
851
568786.14
2673-50
901
637587.01
2830.58
951
710314.88
2987-65
852
570123.67
2676.64
902
639003.09
2833.72
952
711809.50
2990.80
853
571462.77
2679-78
903
640420.73
2836.86
953
713305.68
2993-94
854
572803.4s
2682.92
904
641839-95
2840.00
954
714803.43
2997.08
855
574145-69
2686.06
905
643260.73
2843.14
955
716302.76
3000.22
856
575489-51
2689.20
906
644683.09
2846.28
956
717803.66
3003.36
857
576834-90
2692.34
907
646107.01
2849.42
957
719306.12
3006.50
858
578181.85
2695-49
908
647532.51
2852.57
958
720810.16
3009.6s
859
579530.38
2698.63
909
648959.58
2855.71
959
722315.77
3012.79
860
580880.48
2701.77
910
650388.22
2858.85
960
723822.95
3015.93
861
582232.15
2704.91
911
651818.43
2861.99
961
725331.70
3019.07
862
583585-39
2708.05
912
653250.21
2865.13
962
726842.02
3022.21
863
584940.20
2711.19
913
654683.56
2868.27
963
728353.91
3025.3s
864
586296.59
2714-34
914
656118.48
2871.42
964
729867.37
3028.50
865
587654.54
2717-48
91S
657554.98
2874-56
96s
731382.40
3031-64
866
589014.07
2720.62
916
658993.04
2877.70
966
732899.01
3034-78
867
590375-16
2723.76
917
660432.68
2880.84
967
734417.18
3037-92
868
591737-83
2726.90
918
661873-88
2883.98
968
735936.93
3041.06
869
593102.06
2730.04
919
663316.66
2887.12
969
737458.24
3044-20
870
594^67.87
2733.19
920
664761.01
2890.27
970
738981.13
3047.34
^7^
595835-25
2736.33
921
666206.92
2893.41
971
740505.59
3050.49
872
597204.20
2739-47
922
667654.41
2896.55
972
742031.62
3053.63
873
598574-72
2742-61
923
669103.47
2899.69
973
743559.22
3056.77
874
599946-81
2745-75
924
670554.10
2902.83
974
745088.39
3059-91
875
601320.47
2748-89
925
672006.30
2905.97
975
746619.13
3063.05
876
602695.70
2752.04
926
673460.08
2909.11
976
748151.44
3066.19
877
604072.50
2755.18
927
674915.42
2912.26
•977
749685.32
3069.34
878
605450.88
2758.32
928
676372.33
2915.40
978
751220.78
3072.48
879
606830.82
2761.46
929
677830.82
2918.54
979
752757.80
3075.62
880
608212.34
2764.60
930
679290.87
2921. 68
980
754296.40
3078.76
881
609595-42
2767-74
931
680752.50
2924.82
981
755836.59
3081.90
882
610980.08
2770.88
932
682215.69
2927.96
982
757378.30
3085.04
883
612366.31
2774-03
933
683680.46
2931. II
983
758921.61
3088.19
884
613754-11
2777.17
934
685146.80
2934.25
984
760466.48
3091.33
88s
615143.48
2780.31
935
686614.71
2937.39
98s
762012,93
3094.47
886
616534-42
2783.45
936
688084.19
2940.53
986
763560.95
3097.61
887
617926.93
2786.59
937
689555-24
2943.67
987
765110.54
3100.7s
888
619321.01
2789.73
938
691027.86
2946.81
988
766661.70
3103.89
889
620716.66
2792.88
939
692502.05
2949.96
989
768214.44
3107.04
890
622113.89
2796.02
940
693977.82
2953.10
990
769768.74
3110.18
891
623512.68
2799.16
941
695455.15
2956.24
991
771324-61
3113.32
892
624913.04
2S02.30
942
696934.06
2959.38
992
772882.06
3116.46
893
626314.98
2805.44
943
698414.53
2962.52
993
774441-07
3119.60
894
62771S.49
2808.58
944
699896.58
2965.66
994
776001.66
3122.74
895
629123.56
2811.73
945
701380.19
2968.81
995
777563-82
3125-88
896
630530.21
2814.87
946
702865.38
2971.95
996
779127.54
3129.03
897
631938.43
2818.01
947
704352.14
2975.09
997
780692.84
3132.17
898
633348.22
2821.15
948
705840.47
2978.23
998
782259.71
3135.31
899
634759.58
2824.29
949
707330.37
2981.37
999
783828.15
3138.4s
1
IOOO
785398-16
3141.59
5 lit GENERAL REFERENCE TABLES
Circumferences and Diameters of Circles
Cir-
Diameter
Cir-
Diameter
Cir-
Diameter
Cir-
Diameter
cum.
cum.
cum.
cum.
I
.3183
51
16.2338
lOI
32.1493
151
48.0648
2
.6366
52
16.5521
102
32.4676
152
48.3831
3
•9549
53
16.8704
103
32.7859
153
48.7014
4
1.2732
54
17.1887
104
33.1042
154
49.0197
I-59I5
55
17.5070
105
33.4225
155
49-3380
6
1.9099
56
17.8254
106
33.7408
156
49-6563
7
2.2282
57
18.1437
107
34-0592
157
49-9747
8
2.5465
58
18.4620
108
34-3775
158
50.2930
9
2.8648
59
18.7803
109
34-6958
159
50.6113
lO
3.1831
60
19.0986
no
35-0141
160
50.9296
II
3.5014
61
19.4169
III
35-3324 '
161
S1.2479
12
3-8197
62
19.7352
112
35-6507
162
51.5662
13
4.1380
63
20.0535
113
35-9690
163
51.8845
14
4-4563
64
20.3718
114
36.2873
164
52.2028
15
4.7746
65
20.6901
115
36.6056
165
52.5211
i6
5.0930
66
21.00S5
116
36.9239
166
52.8394
17
5.4113
67
21.3268
117
37.2423
167
53.1578
i8
5.7296
68
21.6451
118
37-5606
168
53.4761
19
6.0479
69
21.9634
119
37.8789
169
53-7944
20
6.3662
70
22.2817
120
38.1972
170
54.1127
21
6.6845
71
22.6000
121
38.5155
171
54-4310
22
7.0028
72
22.9183
122
38.8338
172
54-7493
23
7.3211
73
23.2366
123
39-1521
173
55-0676
24
7.6394
74
23-5549
124
39-4704
174
55-3859
25
7-9577
75
23-8732
125
39-7887
175
55.7042
26
8.2761
76.
24.1916
126
40.1070
176
56.022s .
27
8.5944
77
24.5099
127
40.4254
177
56.3408
28
8.9127
78
24.82S2
128
40-7437
178
56.6592
29
9-2310
79
25-1465
129
41.0620
179
56.9775
30
9-5493
80
25-4648
130
41.3803
180
57.2958
31
9.8676
81
25-7831
131
41.6986
181
. 57.6141
32
10.1859
82
26.1014
132
42.0169
182
57-9324
33
10.5042
83
26.4197
133
42.3352
183
58.2507
34
10.8225
84
26.7380
134
42.653s
184
58.5690
35
II. 1408
85
27.0563
135
42.9718
185
58.8873
36
11.4592
86
27-3747
136
43.2901
186
59.2056
37
11.7775
87
27-6930
137
43-6085
187
59-5239
38
12.0958
88,
28.0113
138
43-9268
188
59-8423
39
12.4141
89
28.3296
139
44.2451
189
60.1606
40
12.7324
90
28.6479
140
44.5634
190
60.4789
41
13.0507
91
28.9662
141
44.8817
191
60.7972
42
13-3690
92
29.2845
142
45.2000
192
61.115s
43
13-6873
93
29.6028
143
45-5183
193
61.4338
44
14.0056
94
29.9211
144
45.8366
194
61.7521
45
14-3239
95
30.2394
145
46.1549
195
62.0704
46
14.6423
96
30.5577
146
46.4732
196
62.3887
47
14.9606
97
30.8761
147
46.7916
197
62.7070
48
15,2789
98
31.1944
148
47-1009
198
63.0254
49
15,5972
99
31-5127
149
47.4282
199
63.3437
50
15.9155
100
31.8310
150
47.746s
200
63.6620
RECIPROCALS
Reciprocals of Numbers from i to iooo
515
No.
Reciprocal
No.
Reciprocal
No.
Reciprocal
No.
Reciprocal
I
1. 00000000
51
.01960784
lOI
.00990099
151
.00662252
2
.50000000
52
.01923077
102
.00980392
152
.00657895
3
.33333333
53
.01886792
103
.00970874.
153
.00653595
4
.25000000
54
.01851852
104
.00961538
154
.00649351
5
.20000000
55
.01818182
los
.00952381
155
.00645161
6
.16666667
56
.01785714
106
.00943396
156
.00641026
7
.14285714
57
.01754386
107
.00934579
157
.00636943
8
.12500000
58
.01724138
108
.00925926
158
.00632911
9
.iiiiiiii
59
.01694915
109
.00917431
1.59
.00628931
10
.10000000
60
.01666667
no
.00909091
160
.00625000
II
.09090909
61
.01639344
III
.00900901
161
.00621118
12
•08333333
62
.01612903
112
.00892857
162
.00617284
13
.07692308
63
.01587302
"3
.00884956
163
.00613497
14
.07142857
64
.01562500
114
.00877193
164
.00609756
15
.06666667
65
.01538461
115
.00869565
165
.00606061
16
.06250000
66
.01515151
116
.00862069
166
.00602410
17
■05882353
67
.01492537
117
.00854701
167
.00598802
18
.05555556
68
.01470588
118
.00847458
168
•00595238
19
.05263158
69
.01449275
119
.00840336
169
.00591716
20
.05000000
70
.01428571
120
.00833333
170
.00588235
21
.04761905
71
.01408451
121
.00826446
171
.0058479s
22
•04545455
72
.01388889
122
.00819672
172
•00581395
23
.04347826
73
.01369863
123
.00813008
173
•0057803s
24
.04166667
74
•01351351
124
.00806452
174
•00574713
25
.04000000
75
•01333333
125
.00800000
175
.00571429
26
.03846154
76
.01315789
126
.00793651
176
.00568182
27
•03703704
77
.01298701
127
.00787402
177
.C0564972
28
.03571429
78
.01282051
128
.00781250
178
.00561798
29
.03448276
79
.01265823
129
•00775194
179
•00558659
30
■03333333
80
.01250000
130
.00769231
180
•00555556
31
.03225806
81
.01234568
131
.00763359
181
.00552486
32
.03125000
82
.01219512
132
•00757576
182
.00549451
33
•03030303
83
.01204819
133
.00751880
183
.00546448
34
.02941176
84
.01190476
134
.00746269
184
.00543478
35
.02857143
85
.01176471
135
.00740741
185
.00540540
36
.02777778
86
.01162791
136
.00735294
186
•00537634
37
.02702703
87
.01149425'
137
.00729927
187
•00534759
38
.02631579
88
.01136364
138
.00724638
188
.00531914
39
.02564103
89
•01123595
139
.00719424
189
.00529100
40
.02500000
90
.OIIIIIII
140
.00714286
190
.00526316
41
.02439024
91
.01098901
141
.00709220
191
.00523560
42
.02380952
92
.01086956
142
.00704225
192
, .00520833
43
.02325581
93
.01075269
143
.00699301
193
.00518135
44
.02272727
94
.01063830
144
.00694444
19^ '
.00515464
45
.02222222
95
.01052632
145
.00689655
I9b
.00512820
46
.02173913
96
.01041667
146
.00684931
196
.00510204
47
.02127660
97
.01030928
147
.00680272
197
.00507614
48
•02083333
98
.01020408
148
.00675676
198
.00505051
49
.02040816
99
.OIOIOIOI
149
.00671141
199
.00502513
SO
.02000000
100
.01000000
150
.00666667
200
.00500000
5i6 GENERAL REFERENCE TABLES
Reciprocals of Numbers from i to iooo
No.
Reciprocal
No.
Reciprocal
No.
Reciprocal
No.
Reciprocal
20I
.00497512
«
251
.00398406
301
.00332226
351
.00284900
202
.00495049
252
.00396825
302
.00331126
352
.00284091
203
.00492611
253
.00395257
303
.00330033
353
.00283286
204
.00.^90196
- 254
.00393701
304
.00328947
354
.00282486
205
.00487805
255
.00392157
305
.00327869
355
.00281690
206
.00485437
256
.00390625
306
.00326797
356
.00280899
207
.00483092
257
.00389105
307
.00325733
357
.00280112
208
.00480769
25S
.00387597
308
.00324675
358
.00279330
2og
.00478469
259
.00386100
309
.00323625
359
.00278551
210
.00476190
260
.00384615
310
.00322581
360
.00277778
211
.00473934
261
.00383142
311
.00321543
361
.00277008
212
.00471698
262
.03381679
312
.00320513
362
.00276243
213
.00469484
263
.00380228
313
.00319489
363
.00275482
214
.00467293
264
.00378788
314
.00318471
364
.00274725
215
.00465116
265
•00377358
315
.00317460
365
.00273973
216
.00462963
266
.00375940
316
.00316456
366
.00273224
217
.00460S29
267
.00374532
317
•00315457
^^Jo
.00272480
218
.00458716
268
.00373134
318
.00314465
368
.00271739
219
.00456621
269
.00371747
319
.00313480
369
.00271003
220
.00454545
270
.00370370
320
.00312500
370
.00270270
221
.00452489
271
.00369004
321
.00311526
371
.00269542
222
.00450450
272
.00367647
322
•00310559
372
.00268817
223
.00448430
273
.00366300
323
•00309597
373
.00268096
224
.00446429
274
.00364963
324
.00308642
374
.00267380
225
.00444444
275
.00363636
325
.00307692
375
.00266667
226
.00442478
276
.00362319
326
.00306748
376
.00265957
227
.00440529
277
.00361011
327
.00305810
377
.00265252
228
.00438596
278
.00359712
328
.00304878
378
.00264550
229
.00436681
279
.00358423
329
.00303951
379
.00263852
230
.00434783
280
.00357143
330
.00303030
380
.00263158
231
.00432900
281
.00355872
331
.00302115
381
.00262467
232
.00431034
282
.00354610
332
.00301205
382
.00261780
233
.00429184
283
•00353357
3S3
.00300300
383
.00261097
234
.00427350
284
.00352113
334
.00299401
384
.00260417
235
.00425532
285
.00350877
335
.00298507
385
.00259740
236
.00423729
286
.00349650
336
.00297619
386
.00259067
237
.00421941
287
.00348432
.337
.00296736
387
.00258398
238
.00420168
288
.00347222
338
.00295858
388
.00257732 '
239
.00418410
289
.00346021
339
.00294985
389
.00257069
240
.00416667
290
.00344828
340
.00294118
390
.00256410
241
.00414938
291
.00343643
341
.00293255
391
.00255754
242
.00413223
292
.00342466
342
.00292398
392
.00255102
243
.00411523
293
.00341297
343
.00291545
393
.00254*453
244
.00409836
294
.00340136
344
.00290698
394
.00253807
245
.0040S163
295
.00338983
345
.00289855
395
.00253165
246
.00406504
296
.00337838
346
.00289017
396
.00252525
247
.00404858
297
.00336700
347
.00288184
397
.00251889
248
.00403226
298
.00335570
348
.00287356
398
.00251256
249
.00401606
299
.00334448
349
.00286533
399
.00250627
250
.00400000
3CO
.00333333
350
.00285714
400
.00250000
RECIPROCALS
Reciprocals of Numbers from ioo to iooo
517
No.
Reciprocal
No.
Reciprocal
No.
Reciprocal
No.
Reciprocal
401
.00249377
451
.00221729
501
.00199601
551
.00181488
402
.00248756
452
.00221239
502
.00199203
552
.00181159
403
.00248139
. 453
.00220751
503
.00198807
553
.00180832
404
.00247525
454
.00220264
■ 504
.00198413
554
.00180505
40s
■ .00246914
45s
.00219780
505
.00198020
555
.00180180
406
.00246305
456
.00219298
506
.00197628
556
.00179856
407
.00245700
457
.00218818
507
.00197239
557
.00179533
408
.00245098
458
.00218341
508
.00196850
558
.00179211
409
.00244499
459
.00217865
509
.00196464
559
.00178891
410
.00243902
460
.00217391
510
.00196078
560
.00178571
4H
.00243309
461
.00216920
S"
.00195695
561
.00178253
412
.002427 iS
462
.00216450
512
.00195312
562
.00177936
413
.00242131
463
.00215983
S13
.00194932 '
563
.00177620
414
.00241546
464
.00215517
514
.00194552
564
■0017730S
415
.00240964
465
.00215054
515
.00194175
565
.00176991
416
.00240385
466
.00214592
516
.00193798
566
.00176678
417
.00239808
467
.00214133
517
.00193424
567
.00176367
418
.00239234
468
.00213675
518
.00193050
568
.00176056
419
.00238663
469
.00213220
519
.00192678
569
.00175747
420
.00238095
470
.00212766
520
.00192308
570
.00175439
421
.00237530
471
.00212314
521
.00191939
571
.00175131
422
.00236967
472
.00211864
522
.00191571
572
.00174825
423
.00236407
473
.00211416
523
.00191205
573
.00174520
424
.00235849
474
.00210970
524
.00190840
574
.00174216
425
.00235294
475
.00210526
525
.00190476
575
.00173913
426
.00234742
476
.00210084
526
.00190114
576
.00173611
427
.00234192
477
.00209644
527
.00189753
577
.00173310
428
.00233645
478
.00209205
528
.00189394
578
.00173010
429
.00233100
479
.00208768
529 •
.00189036
579
.00172712
430
.00232558
480
.00208333
530
.00188679
580
.00172414
431
.00232019
481
.00207900
531
.00188324
581
.00172117
432
.00231481
482
.00207469
532
.00187970
582
.00171821
433
.00230947
483
.00207039
533
.00187617
583
.00171527
434
.00230415
484
.00206612
534
.00187266
584
.00171233
435
.00229885
485
.00206186
535
.00186916
585
.00170940
436
.00229358
486
.00205761
536
.00186567
586
.00170648
437
.00228833
487
.00205339
537
.00186220
587
.00170358
438
.00228310
488
.00204918
538
.00185874
588
.00170068"
43Q
.00227790
489
.00204499
538
.00185528
589
.00169779
440
.00227273
490
.00204082
S40
.00185185
590
.00169491
441
.00226757
491
.00203666
541
.00184843
591
.00169205
442
.00226244
492
.00203252
542
.00184502
592
.00168919
443
.00225734
493
.00202840
543
.00184162
593
.00168634
444
.00225225
494
.00202429
544
.0.0183823
594
.00168350
445
.00224719
495
.00202020
545
.00183486
595
.00168067
446
.00224215
496
.00201613
546
.00183150
.00167785
447
.00223714
497
.00201207
547
.00182815
597
.00167504
448
.00223214
498
.00200803
548
.00182482
598
.00167224
449
.00222717
499
.00200401
549
.00182149
599
.00166945
450
.00222222
SOD
.00200000
550
.00181818
600
.00166667
5l8 GENERAL REFERENCE TABLES
Reciprocals of Numbers from i to iooo
No.
Reciprocal
No.
Reciprocal
No.
Reciprocal
No.
Reciprocal
6oi
:ooi66389
6si
.00153610
701
.00142653
751
.00133156
602
.00166113
652
•OOIS3374
702
.00142450
752
.00132979
603
.00165837
653
.00153140
703
.00142247
753
.00132802
604
.00165563
654
.00152905 .
704
.0014204s
754
.00132626
60s
.00165289
655
.00152672
705
.00141844
755
.00132450
606
.00165016
656
.00152439
706
.00141643
756
.0013227s
607
.00164745
657
.00152207
707
.00141443
757
.00132100
608
.00164474
658
.00151975
708
.00141243
758
.00131926
609
.00164204
659
.00151745
709
.00141044
759
.00131752
610
.00163934
660
.00151515
710
.00140845
760
.00131579
611
.00163666
661
.00151286
711
.00140647
761
.00131406
612
.00163399
662
.00151057
712
.00140449
762
.00131234
613
.00163132
663
.00150830
713
.00140252
763
.00131062
614
.00162866
664
.00150602
714
.00140056
764
.00130890
61S
.00162602
665
.00150376
715
.00139860
765
.00130719
616
.00162338
666
.00150150
716
.00139665
766
.00130548
617
.00162075
667
.00149925
717
.00139470
767
.00130378
618
.00161812
668
.00149701
718
.00139276
768
.00130208
619
.00161551
669
.00149477
719
.00139082
769
.00130039
620
.00161290
670
.00149254
720
.00138889
770
.00129870
621
.00161031
671
.00149031
721
.00138696
771
.00129702
622
.00160772
672
.00148809
722
.00138504
772
.00129534
623
.00160514
673
.00148588
723
.00138313
773
.00129366
624
.00160256
674
.00148368
724
.00138121
774
.00129199
62s
.00160000
67s
.00148148
725
.00137931
775
.00129032
626
.00159744
676
.00147929
726
.00137741
776
.00128866
627
.00159490
677
.00147710
727
.00137552
777
.00128700
628
.00159236
678
.00147493
728
•00137363
778
.00128535
629
.00158982
679
.00147275
729
.00137174
779
.00128370
630
.00158730
680
.00147059
730
.00136986
780
.00128205
631
.00158479
681
.00146843
731
.00136799
781
.00128041
632
.00158228
682
.00146628
732
.00136612
782
.00127877
633
.00157978
^83
.00146413
733
.00136426
783
.00127714
634
.00157729
684
.00146199
734
.00136240
784
. .00127551
635
.00157480
685
.00145985
735
.00136054
78s
.00127388
636
.00157233
686
.00145773
736
.00135870
786
.00127226
637
.00156986
687
.00145560
737
.00135685
787
.00127065
638
.00156740
688
.00145349
738
.00135501
788
.00126904
639
.00156494
689
.00145137
739
.00135318
789
.00126743
640
.00156250
690
.00144927
740
.00135135
790
.00126582
641
.00156006
691
.00144718
741
-00134953
791
.00126422
642
.00155763
692
.00144509
742
.00134771
792
.00126263
643
.00155521
693
.00144300
743
.00134589
793
.00126103
644
.00155279
694
.00144092
744
.00134409
794
.00125945
64s
.00155039
695
;ooi43885
745
.00134228
795
.00125786
646
.00154799
696
.00143678
746
.00134048
796
.00125628
647
.00154559
697
.00143472
747
.00133869
797
.00125470
648
.00154321
698
.00143266
748
.00133690
798
.00125313
649
.00154083
699
.00143061
749
.00133511
799
.00125156
650
.00153846
700
.0014^857
750
.00133333
800
.00125000
RECIPROCALS
Reciprocals of Numbers from i to iooo
519
No.
Reciprocal
No.
Reciprocal
No.
Reciprocal
No.
Reciprocal
801
.00124844
851
.00117509
901
.00110988
951
.00105152
802
.00124688
852
.00117371
902
.00110865
952
.00105042
803
.00124533
853
.00117233
903
.00110742
953
.00104932
804
.00124378
854
.00117096
904
.00110619
954
.00104822
80s
.00124224
855
.00116959
905
.00110497
955
.00104712
806
.00124069
856
.00116822
906
.00110375
956
.00104602
807
.00123916
857
.00116686
907
.00110254
957
.00104493
808
.00123762
858
.00116550
908
.00110132
958
.00104384
809
.00123609
859
.00116414
909
.OOIIOOII
959
.00104275
810
.00123457
860
.00116279
910
.00109890
960
.00104167
811
.00123305
861
.00116144
911
.00109769
961
.00104058
812
.00123153
862
.00116009
912
.00109649
962
.00103950
813
.00123001
863
.00115875
913
.00109529
963
.00103842
814
.00122850
864
.00115741
914
.00109409
964
.00103734
815
.00122699 '
865
.00115607
915
.00109290
965
.00103627
816
.00122549
866
•00115473
916
.00109170
966
.00103520
817
.00122399
867
.00115340
917
.00109051
967
.00103413
818
.00122249
868
.00115207
918
.00108932
968
.00103306
8i9
.00122100
869
.00115075
919
.00108814
969
.00103199
820
.00121951
870
.00114942
9-20
.00108696
970
.00103093
821
.00121803
87^
.0011481 I
921
.00108578
971
.00102987
822
.00121654
872
.00114679
922
.00108460
972
.00102881
823
.00121507
873
.00114547
923
.00108342
973
.00102775
824
.00121359
874
.00114416
924
.00108225
974
.00102669
825
.00121212
875
.00114286
925
.00108108
975
.00102564
826
.00121065
876
.00114155
926
.00107991
976
.00102459
827
.00120919
877
.00114025
927
.00107875
977
.00102354
828
.00120773
878
.00113895
928
.00107759
978
.00102250
829
.00120627
879.
.00113766
929
.00107643
979
.00102145
830
.00120482
880
.00113636
930
.00107527
980
.00102041
831
.00120337
881
.00113507
931
.00107411
981
.00101937
832
.00120192
882
.00113379
932
.00107296
982
.00101833
833
.00120048
883
.00113250
933
.00107181
983
.00101729
834
.00119904
884
.00113122
934
.00107066
984
.00101626
835
.00119760
885
.00112994
935
.00106952
985
.00101523
836
.00119617
886
.00112867
936
.00106838
986
.00101420
837
.00119474
887
.00112740
937
.00106724
987
.00101317
838
.00119332
888
.00112613
938
.00106610
988
.00101215
839
.00119189
889
.00112486
939
.00106496
989
.00101112
840
.00119048
890
.00112360
940
.00106383
990
.00101010
841
.00118906
891
.00112233
941
.00106270
991
.00100908
842
.00118765
892
.00112108
942
.00106157
992
.00100806
843
.00118624
893
.00111982
943
.00106044
993
.00100705
844
.00118483
894
.00111857
944
.00105932
994
.00100604
845
.00118343
895
.00111732
945
.00105820
995
.00100502
846
.00118203
896
.00111607
946
.00105708
996
.00100402
847
.00118064
897
.00111483
947
.00105597
997
.00100301
848
.00117924
898
.00111359
948
.00105485
998
.00100200
849
.00117786
899
.00111235
949
.00105374
999
.00100100
8so
.00117647
900
.0011 II I I
950
.00105263
IOOO
.00100000
SHOP TRIGONOMETRY
The laying out of angles is sometimes difBcult by ordinary methods
and a little knowledge of shop "trig" is very useful and much easier
than as though we called it by its full name. i
6
7
s/
^~~-^^
"7
/
\
I
' 1
Fig.
Fig.
It is really a system of constants or multipliers based on the fact
that there are always fixed proportions between the sides and angles
of triangles and other figures. Fig. i shows a 30-degree angle with
I, 2 and 3-inch arcs, i c, 2/, and 3 i. It will be found that every
similar measurement is in exact proportion to the radius, thus 2 d
is exactly tvnce the length of i a, and h i is just three times he. So,
if we know the distance a c for a i-inch radius for any angle, a similar
distance as g i for the same angle, will be in exact proportion to the
radius of the circle to one, which is the base. All these parts are
named as shown in Figs. 2,3, and 4.
520
SHOP TRIGONOMETRY
521
The exact proportion of all the various parts have been figured
for each part of a degree that is likely to be needed in ordinary work,
and these figures are given in the tables which follow. These num-
bers are simply multipUers or constants for a radius of one, and for
any other radius we multiply the numbers given by the radius we
are using. These tables form the most accurate means of calculating
many problems as will be shown. These constants can represent
one of anything, inches, feet, meters, or miles, and the answer will
be in the same unit. In tool work they are usually in inches, but
the relation is the same regardless of the unit.
Fig. 4
Fig. 5
Angle is Always Taken each Side of the Center Line as
Shown
Lines 1-3 and 1-7 are called radius of the circle.
1-2 is called cosine of the angle.
4-5 is always the same as cosine of the angle.
2-3 is called the versed sine of the angle.
4-7 "
" co-versed sine
of the angle
2-S "
" sine
" " "
3-6"
7-8 "
" tangent
" co-tangent
<( « tt
1-6 "
" secant
ti et ((
1-8 "
" co-secant
(( « <(
The names always refer to the angle on one side of the center
line and not to the total or included angle. In deahng with a 60-
degree thread we divide this by a center Hne and call the angle 30
degrees in all our calculations. Everything is based on the radius
of a circle, and a i radius is used as this base. Perhaps the three
most important parts are the sine, the tangent, and the secant, these
being 2-5, 3-6, and 1-6 in all three of the figures. From this it
will be seen that the sine is half the chord or the distance from the
radius to the horizontal. The tangent 3-6 is the distance from
^22 SHOP TRIGONOMETRY
the horizontal radius to an extension of the radius at the angle given.
The secant is the distance along the radius from the center to the
tangent. From 2 to 3 is called the versed sine, and is the distance
from the center of the chord to the outer circle.
The angle considered in this work is always less than 90 degrees,
and the angle between the angle used and 90 degrees, or the angle
which is necessary to complete this to 90 degrees is called the com-
plementary angle. In the first case the complementary angle is
60 degrees, in the second case 45 degrees, and in the third case 30
degrees. The co-sine is the distance 4-5) the co-tangent is 7-8, the
co-secant is 1-8, and the co-versed sine is 4-7 in all three examples.
In the 45-degree angle it will be seen that the various parts are alike
in both angles, as the sine is the same as the cosine, while the sine
of the angle of 30 degrees is the same as the cosine of the angle of
60 degrees. These facts will be borne out by the tables and can be
seen by studying the diagrams or by making^ any calculation and
then proving it as near as may be on the drawing board.
All this is interesting, but unless it is useful it has no value to the
practical man, so we will see where it can be used to advantage in
saving time and labor.
Perhaps the easiest application is in finding the depth of a V-
thread without making any figures. The angle is 60 degrees or
30 degrees each side of the center Hne. The pitch is i inch so that
each side is also an inch, and so the radius is an inch, the depth of
the thread is the distance 1-2 or 4-5, and is the cosine of the angle.
Looking in the table for the cosine of the angle of 30 degrees we
find 0.86603, and as the radius is i this gives us the depth directly
as 0.86603 inch. If the radius was 2 inches we would multiply by
2, or if it was \ inch, divide by 2 and get the exact depth with almost
no figuring. Suppose, on the other hand, that the thread was one
inch deep and we want to find the length of one side, the angle re-
maining the same as before. In this case we have the depth which
is the Une 1-3, and we wish to find 1-6 which is the secant, so we
look at the table again and find the secant of 30 degrees to be 1.1547
inches as the length of the side.
Suppose you have a square bar 2^ inches on each side, what is
the distance across the corners? Looking at the second example
we see that the side of the square bar is represented by line 1-3 and
the corner distance by the secant 1-6 so we look for the secant of
45 degrees (because we know that half the 90 degree angle of a square
bar must be 45 degrees) and find 1.4142 which would be the distance
if the bar was one inch square, so we multiply 1.-^142 by 2^ and get
3.5355 inches as the distance across the corners, and can know that
this is closer than we can measure, and is not a guess by any means.
Reversing this we can find the side of a square that can be milled
out of a round bar, such as the end of a reamer or tap. What square
can we make on a 2-inch round reamer shank? The dianieter of
the bar is the radius as 1-5 and the angle 45 degrees as before, half
the side of the square will be the sine 2-5, which the table shows
to be 0.70711, and as this is half the chord wliich makes the mt
across the bar, we multiply this by 2 and get i. 41422 inches as we
distance across the flats for a reamer shank of this size.
SHOP TRIGONOMETRY
523
Suppose we have a bar of i| X f-inch steel and want to find the
distance across the comers, and the angle it will make with the base.
The ij-inch side is the radius, the diagonal is the secant, and the
f-inch side is the tangent of the angle. Reducing these to a basis
of one inch we have a bar i inch by h inch and the J inch is the tan-
gent of the angle. Looking in the table we find this to be almost
exactly the tangent of 26 degrees and 34 minutes. With this angle
the secant or diagonal
is 1. 1 1 80 for a radius of
I inch and i^ times this
gives 1.6770 as the dis-
tance across comers.
A very practical use
for this kind of calcula-
tion is in spacing bolt
holes or otherwise divid-
ing a circle into any
number of equal parts.
Fig. 6 It is easy enough to get
the length of each arc of
the circumference by di-
viding 360 degrees by
the number of divisions,
but what we want is to
find the chord or the dis-
tance from one point to
the next in a straight
line as a pair of dividers
would step it off. First
divide 360 by the num-
ber of divisions — say 9
■ — and get 40 degrees in
each part. Fig. 5 shows
this and we want the
distance shown or the
chord of the angle. This
equals twice the sine of
half the angle. Half the
angle is 20 degrees and
the sine for this is .342.
Twice this or 0.684 is
the chord of the 40-de-
gree angle for every inch
of radius. If the circle is 14 inches in diameter the distance between
the holes will be 7 times 0.684 or 4.788 inches. This is very quick
and the most accurate method known.
Draftsmen often lay out jigs with the angles marked in degrees
as in Fig. 6, overlooking the fact that the toolmaker has no conven-
ient or accurate protractor for measuring the angle. Assume that a
drawing shows three hohs as a, b, and c, with b and c 20 degrees
apart. The distance from a to & is 3 inches, what is the distance
fcrom 6 to c or from a to c?
Fig. 7
524
SHOP TRIGONOMETRY
As the known radius is from a to 6, the distance b c is the tangent
of the angle and the tangent for a one-inch radius is .36397, so for a
3-inch radius it is 3 X .36397 = 1.09191 inches from 6 to c and at
right angles to it.
But we need not depend on the accuracy of the square or of the
way we use it, as we can find the distance from a to c just as easily
and just as accurately as we did b c. This distance is the secant,
and is 1.0642 for a one-inch radius. Multiplying this by 3 = 3.1926
as the distance which can be accurately measured.
If the distance between a and c had been 3 inches, then b c would
have been the sine and a b the cosine of the angle, both of which can
be easily found from the tables.
It often happens that we want to find the angle of a roller or other
piece of work as Fig. 7. Always work from the center line and con-
tinue the Unes to complete the angle. Every triangle has the sides
and they are called the "side opposite," "side adjacent," and "hy-
potenuse," the first being opposite the angle, the second the base
line, and the third the slant line.
The following rules are very useful in this kind of work:
(2) Cosine =
(3) Tangent
(6) Side Opp. = Hypot. X Sine.
(7) Side Adj. =.Hypot. X Cosine.
(8) Side Opp. = Side Adj. X Tangent.
Side Opp.
(i) Sme = —rj — -P-
^ ^ Hypot.
Side Adj.
Hypot.
_ Side Opp.
Side Adj.
(4) Co-Tangent = g!^^^"^^' (9) Side Adj. = Co-Tan. X Side Opp.
, . „ ^ Side Opp. , V TT ^ Side Adj.
(5) Hypot. = -^j;^;^ (10) Hypot. = -^^^r^
If we have the dimensions
shown in Fig. 7, the side opposite,
and the hypotenuse, we use
formula No. i,and dividing 2 by
4 we get I or .5 as the sine of the
angle-. The table shows this to be
the sine of the angle of 30 degrees,
consequently this is a 30-degree
angle.
If we have the side opposite
and the side adjacent we use
formula No. 3, and find that f =
J or .5 = the tangent of the angle.
The table shows this to be the tangent of 26 degrees and 34 minutes.
Should it happen that we only knew the hypotenuse and the angle
we use formula No. 6 and multiply 4 X .5 = 2, the side opposite.
In the same way we can find the side adjacent by using formula
No. 7. The cosine of 30 degrees is .866 and 4 X .866 = 3.464
inches as the side adjacent.
Having a bar of steel 2 by 3 inches. Fig. 8, what is the distance
across the comers? Either formulas 3 or 4 will answer for this.
Fig. 8
TABLE OF REGULAR POLYGONS
525
Taking No. 4 we have 2 as the side opposite, 3 as the side adjacent.
Dividing 3 by 2 gives 1.5. Looking under co-tangents for this we
find 1.5003 after :^s degrees 41 minutes, which is nearly the correct
angle. Then look for the secant of this and find 1.2017. Multiply
this by 3 and get 3.6051 as the distance across the corners.
Complete tables of sines, tangents, secants, etc., will be on pages
529 to 563,
USING THE TABLE OF REGULAR POLYGONS
The easiest way to lay out figures of this kind is to draw a circle
and space it off, but it saves lots of time to know what spacing to use
or how large a circle to draw to get a figure of the right size. Suppose
we wish to lay out any regular figure, such as pentagon or five -sided
figure, having sides ij inches long.
-SSa
*J 0 *J
■p m:2
£<}> "
S-2
^^
•^-^
•sp^ng
^7^'^
-^ S.
■^ ?.
tUO 3 S
1
S
"11
fe & ?
Ms
^ C 3
II
111
II
^
^
S
Q
<:
<
H
3
Triangle . .
1.1546
.5774
.866
1-732
120°
60°
.4330
4
Square
1.4142
I.
.7071
I.
90
90
I.
.S
Pentagon . .
1. 7012
1-3764
.5878
•7265
72
108
1.7204
6
Hexagon . .
2.
1.732
.5
•5774
60
120
2.5980
7
Heptagon .
2.3048
2.0766
.4338
.4815
Si°-26'
128 f
3-6339
8
Octagon . . .
2.6132
2.4142
.3827
.4142
45
135
4.8284
9
Nonagon . .
2.9238
2.7474
.342
.3639
40
140
6.1818
10
Decagon . .
3-236
3.0776
•309
•3247
36
144
7.6942
II
Un decagon
3-5494
3.4056
.2817
.2936
32"-43
I47TT
9-3656
12
Dodecagon
3-^638
3-732
.2588
.2679
30
150
11.1961
Table of Regular Polygons
Looking in the third column we find "Diameter of circle that will
just enclose it," and opposite pentagon we find 1.7012 as the circle
that will just enclose a pentagon ha\ing a side equal to i. This
may be i inch or i anything else, so as we are dealing in inches we
call it inches. As the side of the pentagon is to be i^ inches we
multiply 1. 701 2 by 1 1 and get 2.5518 as the diameter of circle to draw,
and take half of this or the radius 1.2759 in the compass to draw
the circle. Then with i§ inches in the dividers we space round
circle, and if the work has been carefully done it will just divide it
into five equal parts. Connect these points by straight lines, and
you have a pentagon with sides i| inches long.
526 SHOP TRIGONOMETRY
If the pentagon is to go inside a circle of given diameter, say 2
inches, look under column 5 which gives " Length of side when diam-
eter of enclosing circle equals i," and find 5878. Multiply by 2 as
this is for a 2-inch circle, and the side will be 2 X '5878 = 1.1756.
Take this distance in the dividers and step around the 2-inch circle.
Assume that it is necessary to have a triangular end on a round
shaft, how large must the shaft be to give a triangle 1.5 inches on
a side?
Look in the table under column 3, and opposite triangle find
1. 1546, meaning that where the side of a triangle is i, the diameter
of a circle that will just enclose it is 1.1546. As the side is 1.5, we
have 1.5 X 1-1546 = 1.7318, the diameter of the shaft required.
If the corners need not be sharp probably a shaft 1.625 would
be ample.
Reversing this to find the size of a bearing that can be turned on
a triangular bar of this size, look in column 4, which gives the
largest circle that will go inside a triangle with a side equal to i.
This gives .5774. Multiply this by 1.5 = .8661.
A square taper reamer is to be used which must ream i inch at
the smaU end and 1.5 at the back, what size must this be across the
flats at both places?
Under column 5 find .7071 as the length of the side of a square
when the diameter of the enclosing circle is i , so this will be the side
of the small end of the reamer and 1.5 X -7071 = 1.0606 is the
side of the reamer at the large end.
FINDING THE RADIUS WITHOUT THE CENTER
It sometimes happens in measuring up a machine that we need
to know the radius of curves when the center is not accessible.
Three such cases are shown in Figs. 9, 10, and 11, the first two being
a machine and the last a broken pulley. In Fig. 9 the rule is short
enough to go in the curve while in Fig. 10 it has one end touching
and the other across the sides. It makes no difference which is
used so long as the distances are measured correctly, the short dis-
tance or versed sine being taken at the exact center of the chord
and at right angles to it. It is easier figuring when the chord or the
hight are even inches, so in measuring shp the rule until one or the
other comes even; sometimes it is better to make the hight come
I inch and let the chord go as it will, while at others the reverse may
be true. The rule for finding the -diameter is: Square half the chord,
add to this the square of the hight, and divide the whole thing by
the hight.
If the chord is 6 inches, as in Fig. 9, and the hight i| inches we have
i chords + hight^ _ f+ iP _ 9 + 2I _ III == yi inches,
hight i| i^ li ^
Or as shown in Fig. 10 the chord is 10 inches and the hight i inch,
then the figures are
£!±i' = £i±i = 26 inches.
I I
PROPERTIES OF REGULAR FIGURES
527
In Fig. II we have a piece of a broken pulley, and find the chord
B to be 24 inches, and the hight A to be 2 inches. This becomes
= • = = 74, so that the diameter of the pulley is
222
74 inches.
FIG. II
Finding the Radius without Center
PROPERTIES OF REGULAR FIGURES
The Circle
A circle is a continuous curved line having every point at an equal
distance from the center.
Its perimeter or circumference is always 3.14159265359 times the
diameter, although 3.1416 is generally used and 3^ is a very close
approximation.
Area equals the diameter squared X .7854, or half the diameter
squared X 3.1416, or half the diameter X half the circumference.
Diameter of a square having equal area = diameter of circle
times .89 very nearly.
Triangle
Equilateral triangle is a regular figure having three equal sides
and three equal angles of 60 degrees each.
The side equals .866 times the diameter of enclosing circle.
Distance from one side to opposite point equals the side times
.866 or diameter of enclosing circle X .75 or inside circle X li-
Diameter of enclosing circle equals the side times 1.1546 or i^
times distance from side to point or twice inside circle.
Diameter of inside circle equals side times .5774 or | the enclosing
circle.
The area equals one side multiplied by itself and by .433013.
Diameter of circle having equal area equals side of triangle times .73,
528 SHOP TRIGONOMETRY
The Square
A square is a figure with four equal sides and four equal angles
of 90 degrees.
Its perimeter or outside surface is four times the length of one side.
Area equals one side multiplied by the other which is the same as
multiplying by itself or "squaring."
Diagonal or "long diameter," or "distance across comers," equals
the side multiplied by 1.414.
Area of circle that will go inside the square equals one side mul-
tiphed by itself times .7854 or .7854 times the area of the square.
Area of circle that will just enclose the square equals diagonal
multiplied by itself times .7854 or 1,27 times the area of the square.
Diameter of a circle having an equal area is 1.126 or practically
1 1 times the side of the square.
The Hexagon
A hexagon is a regular figure wdth six equal sides and six equal
angles of 120 degrees. It can be drawn inside a circle by spacing
around with the radius of the circle.
The side equals half the diameter of enclosing circle.
The long diameter eqvials diameter of enclosing circle or twice the.
length of one side.
The short diameter equals the long diameter multiplied by .866
or 1.732 times one side.
The area equals one side multiplied by itself and by 2.5981.
The area of enclosing circle is one side multiplied by itself and
by 3.1416.
The area of an inside circle is the short diameter multiplied by
itself and by .7854.
Diameter of circle having equal area is practically .9 times long
diameter.
The Octagon
An octagon is a regular figure with eight equal sides and eight
equal angles of 135 degrees.
The side equals the long diameter multiplied by .382.
The side equals the short diameter multiplied by .415.
The long diameter equals diameter of enclosing circle or one side
multiplied by 2.62.
The short diameter equals the long diameter multiphed by .93,
or one side multiplied by 2.45.
The area equals one side multiplied by itself and by 4.8284.
The area of enclosing circle is 1.126 times area of octagon.
The area of inside circle is .972 times area of octagon.
The diameter of a circle having equal area is .953 times the long
diameter of the octagon.
NATURAL TANGENTS AND CO-TANGENTS 529
0° 1
1
0
.<•
0
'
Tan.
Co-TAN.
Tan. .
Co-tan.
Tan.
Co-TAN.
0
.00000
Infinite.
.01746
57.2900
.03492
28.6363
I
.00029
3437-750
•01775
56.3506
.03521
28.3994
2
.00058
1718.870
.01804
55-4415
•03550
28.1664
3
.00087
1145.920
.01833
54-5613
•03579
27-9372
4
.00116
859-436
.01862
53-7086
.03609
27.7117
5
.00145
687.549
.01891
52.8821
-03638
27-4899
6
.00175
572-957
.01920
52.0807
.03667
27.2715
7
.00204
491.106
.01949
51^3032
.03696
27.0566
8
.00233
429.718
.01978
50-5485
-03725
26.8450
9
.00262
381.971
.02007
49.8157
•03754
26.6367
10
.00291
343-774
.02036
49.1039
•03783
26.4316
11
.00320
312.521
.02066
48.4121
.03812
26.2296
12
.00349
286.478
.02095
47-7395
.03842
26.0307
13
.00378
264.441
.02 1 24
47-0853
.03871
25.8348
14
.00407
245-552
.02153
46.4489
.03900
25.6418
15
.00436
229.182
.02182
45.8294
.03929
25^4517
16
.00465
214.858
.02211
45.2261
■039.58
25.2644
17
.00495
202.219
.02240
44-6386
•03987
25.0798
18
.00524
190.984
.02269
44.0661
.04016
24.8978
19
•00553
180.932
.02298
43.5081
.04046
24^7i85
20
.00582
171-885
.02328
42.9641
•04075
24-5418
21
.00611
163.700
•02357
42-4335
.04104
24-3675
22
.00640
156.259
.02386
41-9158
-04133
24-1957
23
.00669
149.465
•02415
41.4106
.04162
24.0263
24
.00698
143-237
.02444
40.9174
.04191
23-8593
25
.00727
137-507
.02473
40-43.58
.04220
23-6945
26
•00756
132.219
.02502
39-9655
.04250
23-5321
27
.00785
127.321
•02531
39-5059
.04279
23-3718
28
.00814
122.774
.02560
39.0568
.04308
23.2137
29
.00844
118.540
.02589
38-6177
•04337
23-0577
30
.00873
114-589
.02619
38.1885
.04366
22.9038
31
.00902
110.892
.02648
37-7686
-04395
22.7519
32
.00931
107.426
.02677
37-3579
.04424
22.6020
Zl
.00960
104.171
.02706
36-9560
.04454
22.4541
34
.00989
101.107
•02735
36-5627
.04483
22.3081
35
.01018
98.2179
.02764
36-1776
.04512
22.1640
36
.01047
95 4895
•02793
35 -8006
•04541
22.0217
H
.01076
92.9085
.02822
35^4313
-04570
21.8813
38
.01105
90-4633
.02851
35-0695
.04599
21.7426
39
•01 1 35
88.1436
.02881
34-7151
.04628
21.6056
40
.01164
85-9398
.02910
34-3678
.04658
21.4704
41
.01193
83-8435
•02939
34-0273
.04687
21.3369
42
.01222
81.8470
.02068
33-6935
.04716
21.2049
43
.01251
79-9434
.02997
33-3662
•04745
2 1. 0747
44
.01280
78.1263
.03026
33-0452
•04774
20.9460
45
•01309
76.3900
•03055
32.7303
.04803
20. 8 1 88
46
•01338
74.7292
.03084
32.4213
.04832
20.6932
47
•01367
73 -1390
.03114
32.1181
.04862
20.5691
48
.01396
71.6151
•03143
31.8205
.04891
20.4465
49
.01425
70.1533
.03172
31-5284
.04920
20.3253
50
•01455
68.7501
.03201
31.2416
•04949
20.2056
51
.01484
67-4019
.03230
30-9599
.04978
20.0872
52
•01513
66.1055
•03259
30-6833
•05007
19.9702
S3
.01542
64.8580
.03288
30.4116
•05037
19.8546
54
.01571
63.6567
•03317
30.1446
.05066
19.7403
55
.01600
62.4992
-03346
29.8823
-05095
19.6273
56
.01629
61.3829
•03376
29.6245
.05124
19-5156
^l
.01658
60.3058
-03405
29.3711
•05153
19.4051
58
.01687
59-2659
•03434
29-1220
.05182
19-2959
59
.01716
58.2612
-03463
28.8771
.05212
19-1879
60
.01746
57-2900
.03492
28.6363
.05241
19.0811
~^
Co-TAN.
Tan.
Co-tan.
Tan.
Co-tan.
Tan.
i
W
8
8<^
8
70
3
0
Tan.
Co-TAN.
. '
.05241
19.0811
60
•05270
18.9755
59
.05299
18.8711
58
.05328
18.7678
57
•05357
18.6656
56
•05387
18.564s
55
.05416
18.4645
54
•05445
18.3655
53
•05474
18.2677
52
•05503
18.1708
51
•05533
18.0750
50
.05562
17.9802
49
•05591
17.8863
48
.05620
17-7934
47
•05649
17.7015
46
•05678
17.6106
4S
.05708
17.5205
44
-05737
17.4314
43
-05766
17^3432
42
•05795
17-2558
41
.05824
17.1693
40
•05854
17-0837
39
•05883
16.9990
38
.05912
16.9150
37
•05941
16.8319
36
•05970
16.7496
35
•05999
16.6681
34
.06029
16.5874
33
.06058
16.507s
32
.06087
16.4283
31
.06116
16.3499
30
-06145
16.2722
29
-06175
16.1952
28
.06204
16.1190
27
-06233
16.0435
26
.06262
15-9687
25
.06291
15-8945
24
.06321
15.8211
23
-06350
15-7483
22
•06379
15.6762
21
.06408
15.6048
20
-06437
15-5340
19
.06467
15-4638
18
.06496
15-3943
17
•06525
15-3254
16
•06554
15-2571
15
.06584
15-1893
14
.06613
15.1222
13
.06642
15-0557
12
.06671
14-9898
II
.06700
14.9244
10
•06730
14-8596
9
.06759
14-7954
8
.06788
14-7317
7
.06817
14-6685
6
.06847
14.6059
S
.06876
14-5438
4
.06905
14-4823
3
.06934
14.4212
2
.06963
14-3607
I
.06993
14.3007
0
Co-TAN.
8
Tan.
6°
'
NATURAL TANGENTS AND CO-TANGENTS
4=
Tan.
Co-tan.
5^
Tan.
)
Co-tan.
6
Tan.
3
Co-TAN.
7
Tan.
3
Co-TAN.
.06993
14.3007
.08749
11.4301
.10510
9.51436
.12278
8.14435
.07022
14.2411
.08778
11.3919
.10540
9.48781
.12308
8.12481
.07051
14.1821
.0S807
11-3540
.10569
9.46141
.12338
8.10536
.07080
14-1235
.08837
11-3163
.10599
9^43515
.12367
8.08600
.07110
14.0655
.08866
11.2789
.10628
9.40904
•12397
8.06674
.07139
14.0079
.08895
11.2417
.10657
9-38307
.12426
8.04756
.07168
13-9507
.08925
11.2048
.10687
9-35724
.12456
8.02848
.07197
13.8940
.08954
11.1681
.10716
9-33154
.12485
8.00948
.07227
13-8378
.08983
11.1316
.10746
9-30599
.12515
7-99058
.07256
13.7821
.09013
11-0954
.10775
9.28058
.12544
7.97176
.07285
13.7267
.09042
11-0594
.10805
9-25530
.12574
7-95302
•07314
13-6719
.09071
11.0237
.10834
9.23016
.12603
7-93438
•07344
13.6174
.09101
10.9882
.10863
9.20516
.12633
7.91582
•07373
13-5634
.09130
10.9529
.10893
9.18028
.12662
7-89734
.07402
13.5098
.09159
10.9178
.10922
9-15554
.12692
7-87895
•07431
13-4566
.09189
10.8829
.10952
9-13093
.12722
7.86064
.07461
13-4039
.09218
10.8483
.10981
9.10646
.12751
7.84242
.07490
13-3515
.09247
10.8139
.11011
g.08211
.12781
7.82428
•07519
13.2996
.09277
10.7797
.11040
9-05789
.12810
7.80622
•07548
13.2480
.09306
10.7457
.11070
9-03379
.12840
7-78825
.07578
13-1969
•09335
10.7119
. 11099
9.00983
.12869
7-77035
.07607
13.1461
•09365
10.6783
.11128
8.98598
.12899
7-75254
.07636
13.0958
•09394
10.6450
.11158
8.96227
.12929
7-73480
.07665
13.0458
•09423
10.6118
.11187
8.9,3867
■^^n^
7-71715
.07695
12.9962
•09453
10.5789
.11217
8.91520
.12988
7-69957
.07724
12.9469
.09482
10.5462
.11246
8.89185
.13017
7.68208
•07753
12.8981
.09511
10.5136
.11276
8.86862
•13047
7.66466
.07782
12.8496
.09541
10.4813
•11305
8.84551
.13076
7.64732
.07812
12.8014
.09570
10.4491
•11335
8.82252
.13106
7.63005
.07841
12.7536
.09600
10.4172
•11364
8.79964
•13136
7.61287
.07870
12.7062
.09629
10.3854
.11394
3-77689
•13165
7-59575
.07899
12.6591
.096=58
10.3538
.11423
8.75425
.13195
7.57872
.07929
12.6124
.09688
10.3224
•11452
8.73172
.13224
7.56176
.07958
12.5660
.09717
10.2913
.11482
8.70931
•13254
7-54487
.07987
12.5199
.09746
10.2602
.11511
8.68701
.13284
7.52806
.08017
12.4742
•09776
10.2294
•11541
8.66482
•13313
7^5ii32
.08046
12.4288
.09805
10,1988
.11570
8.64275
•13343
7^49465
.08075
12.3838
.09834
10.1683
.11600
8.62078
•13372
7.47806
.08104
12.3390
.09864
10.1381
.11629
8.59893
.13402
7.46154
.08134
12.2946
.09893
10.J080
.11659
8.57718
.13432
7^44.S09
.08163
12.2505
•09923
10.0780
.11688
8-55555
.13461
7.42871
.08192
12.2067
.09952
10.0483
.11718
8.53402
•13491
7.41240
.08221
12.1632
.P9981
10.0187
.11747
8.51259
•13521
7.39616
.08251
12.1201
.10011
9-98931
•11777
8.49128
.13550
7-37999
.08280
12.0772
, .10040
9.96007
.11806
8.47007
.13580
7-36389
.08309
12.0346
.10069
9.93101
.11836
8.44806
.13609
7.34786
•08339
11-9923
.10099
9.90211
.11865
8.42795
.13630
7^33iQO
.08368
11.9504
.10128
9-873.?8
.11895
8.40705
.13660
7.31600
.08397
11.9087
.10158
9.84482
.11924
8.3862s
.13698
7.30018
.08427
11.8673
.10187
9.81641
.11954
8.36555
.13728
7.28442
.08456
11.8262
.10216
9.78817
.11983
8.34496
.13758
7-26873
.08485
11-7853
.10246
9.76009
.12013
8.32446
.13787
7^25310
•08514
11.7448
.10275
9.73217
.12042
8.30406
.13817
7^23754
•08544
11.7045
.10305
9.70441
.12072
8.28376
.13846
7.22204
•08573
11.6645
.10334
9.67680
.12101
8.26355
.13876
7.20661
.08602
11.6248
.10363
964935
.12131
8.24345
-13906
7.19125
.08632
11-5853
•10393
9.62205
.12160
8.22344
■13935
''•17594
.08661
11.5461
.10422
9.59490
.12190
8.20352
.13965
7.16071
.08690
11.5072
.10452
9-56791
.12219
8.18370
•13995
7^14553
.08720
11.4685
.10481
9-54106
.12240
8.16398
.14024
7.13042
.08749
11-4301
.10510
9.51436
.12278
8.14435
.14054
7^ii537
Co-tan
' Tan,
1
jCo-TAN
Tan.
Co-tan
Tan.
Co-TAN
Tan.
1 i
55°
84°
11 i
?3°
S
2°
NATURAL TANGENTS AND CO-TANGENTS 531
8
3
9
3
10° !
11°
*
Tan.
Co-tAn.
Tan.
Co-TAN.
Tan.
Co-TAN.
Tan.
Co-TAN.
/
o
.14054
7-II537
.15838
6.3137s
.17633
S-67128
.19438
5-14455
60
I
.14084
7.10038
.15868
6.30189
.17663
5-66165
.19468
5-13658
59
2
.14113
7.08546
.15898
6.29007
.17693
5 -6520s.
.19498
5.12862
58
3
•14143
7.07059
.15928
6.27829
•17723
5.64248
.19529
5.12069
57
4
•14173
7-05579
.15958
6.2665s
.17753
5-63295
.19559
5-11279
56
5
.14202
7.04105
.15988
6.25486
.17783
5-62344
.19589
5-10490
55
6
.14232
7.02637
.16017
6.24321
.17813
5-61397
.19619
5.09704
54
7
.14262
7.01174
.16047
6.23160
.17843
5-60452
.19649
5.08921
53
8
.14291
6.90718
.16077
6.22003
.17873 5-59511
.19680
5-08139
52
9
.14321
6.98268
.16107
6.20851
.17903 1 5-58573
.19710
5.07360
51
lO
.14351
6.96823
.16137
6.19703
•17933 5-57638
.19740
5-06584
50
II
.14381
6.9538s
.16167
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6.82694
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6.06240
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5-46648
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4-97438
38
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6.78564
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6.05143
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6.77199
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31
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3-01783
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2.85023
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3.20079
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2.84229
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3-38679
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3-18127
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3.17804
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2.99447
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2.82914
32
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2.99158
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2.82653
31
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3-37594
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3-17159
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2.98868
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2.82391
30
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3-37234
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3-16838
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2.98580
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2.82130
29
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3-16517
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2.81870
28
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3-36516
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2.98004
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2.81610
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3-36158
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3-15877
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2-97717
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2.81350
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3-15558
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2.97430
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2.8109I
25
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3-35443
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3.15240
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2.97144
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2.80833
24
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3-35087
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3.14922
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2.96858
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2.80574
23
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3-34732
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3.14605
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2-96573
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2.80316
22
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21
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3-33670
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3-13656
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2.95721
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3.13027
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2-79033
17
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2.94872
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2-78778
16
45
.30097
3-32264
.32010
3.12400
•33945
2.94590
•35904
2-78523
IS
46
.30128
3-31914
.32042
3.12087
•33978
2.94309
•35937
2.78269
14
47
.30160
3-31565
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3-11775
•340 lO
2.94028
•35969
2.78014
13
48
.30192
3.31216
.32106
3-11464
•34043
2.93748
.36002
2.77761
12
49
.30224
3-30868
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3-11153
•34075
2.93468
•36035
2.77507
n
50
•30255
3-30521
.32171
3-10842
•34108
2.93189
.36068
2.77254
10
SI
.30287
3-30174
.32203
3-10532
.34140
2.92910
.36101
2.77002
9
52
•30319
3.29829
.32235
3.10223
•34173
2.92632
•36134
2.76750
8
53
■30351
3-29483
.32267
3.09914
•34205
2-92354
•36167
2.76498
7
54
.30382
3-29139
.32299
3.09606
•34238
2.92076
•36199
2.76247
6
55
.30414
3-28795
•32331
3.09298
.34270
2.91799
•36232
2.75996
S
S6
.30446
3.28452
•32363
3-08991
-34303
2-91523
•36265
2.75746
4
57
.30478
3.28109
•32396
3-08685
-34335
2.91246
.36298
2-75496
3
S8
.30509
3.27767
•32428
3-08379
•34368
2.90971
■36331
2-75246
3
59
•30541
3.27426
.32460
3-08073
-34400
2.90696
•36364
2-74997
I
60
•30573
3.27085
.32402
3.07768
-34433
2.90421
■36397
2.74748
0
/
Co-tan.
Tan.
Co-tan. 1 Tan.
Co-tan.
Tan
jCo-TAN.
Tan.
T~
7
3°
7
2° 1
r 7
1°
1 7
0°
534 NATURAL TANGENTS AND CO-TANGENTS
20°
21°
22°
23° 1
/
Tan.
Co-tan.
Tan.
Co-tan.
Tan.
Co-tan.
Tan.
Co-TAN.
o
•36397
2.74748
■38386
2.60509
.40403
2.47509
.42447
2-35585
I
•36430
2.74499
.38420
2.60283
.40436
2.47302
.42482
2-35395
2
•36463
2.74251
■38453
2.60057
.40470
2.47095
.42516
2-35205
3
.36496
2.74004
■38487
2.59831
.40504
2.46888
.42551
2^35015
4
•36529
2.73756
■38520
2.59606
•40538
2.46682
.42585
2.34825
5
.36562
2^73509
■38553
2.59381
.40572
2.46476
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2.34636
6
•36595
2.73263
■38587
2.59156
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2.46270
.42654
2-34447
7
.36628
2.73017
.38620
2.58932
.40640
2.46065
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2-34258
8
.36661
2.72771
■38654
2.58708
.40674
2.45860
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2.34069
9
.36694
2.72526
.38687
2.58484
•40707
2.45655
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2-33881
20
•36727
2.72281
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2.58261
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2^45451
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2-33693
II
.36760
2.72036
•38754
2.58038
•40775
2.45246
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2^33505
12
•36793
2.71792
•38787
2.57815
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2.45043
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2^333i7
13
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2.71548
.38821
2.57593
•40843
2.44839
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2.33130
14
•36859
2.71305
•38854
2.57371
.40877
2.44636
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2-32943
IS
.36892
2.71062
.38888
2-57150
.40911
2-44433
.42963
2-32756
i6
.36925
2.70819
.38921
2.56928
•40945
2.44230
.42998
2-32570
17
•36958
2.70577
■38955
2.56707
.40979
2.44027
■43032
2.32383
i8
.36991
2.70335
.38988
2.56487
.41013
2.43825
.43067
2.32197
19
•37024
2.70094
.39022
2.56266
.41047
2.43623
.43101
2.32012
20
•37057
2.69853
.39055
2.56046
.41081
2.43422
•43136
2.31826
21
.37090
2.69612
.39089
2.55827
.41115
2.43220
.43170
2.31641
22
•37124
2.69371
.39122
2.55608
.41149
2.43019
.43205
2.31456
23
•37157
2.69131
•39156
2.55389
■41 183
2.42819
.43239
2.31271
24
•37190
2.68892
.39190
2.55170
.41217
2.42618
.43274
2.31086
25
•37223
2.68653
.39223
2.54952
.41251
2.42418
.43308
2.30902
26
•37256
2.68414
•39257
2^54734
•41285
2.42218
.43343
2.30718
27
•37289
2. -.8175
.39290
2.54516
.41319
2.42019
.43378
2-30534
28
■37322
2.67937
•39324
2.54299
.41353
2.41819
.43412
2-30351
29
•37355
2.67700
•39357
2.54082
.41387
2.41620
•43447
2.30167
30
.37388
2.67462
•39391
2.53865
.41421
2.41421
.43481
2.29984
31
.37422
2.67225
•39425
2.53648
.41455
2.41223
.43516
2.29801
32
•37455
2.66989
•39458
2.53432
.41490
2.41025
•43550
2.29619
33
•37488
2.66752
.39492
2.53217
•41524
2.40827
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2.29437
34
■37521
2.66516
•39526
2.53001
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2.40629
.43620
2.29254
35
•37554
2.66281
•39559
2.52786
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2.40432
•43654
2-29073
36
.37588
2.66046
•39593
2.52571
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2.40235
•43689
2.28891
37
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2.65811
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2^52357
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2.40038
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2.28710
38
•37654
2.65576
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2.52142
.41694
2.39841
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2.28528
39
•37687
2.65342
.39694
2.51929
.41728
2.39645
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2.28348
40
.37720
2.65109
•39727
2.51715
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2.39449
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2.28167
41
•37754
2.64875
•39761
2.51502
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2.39253
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2.27987
42
•37787
2.64642
■39795
2.51289
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2.39058
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2.27806
43
•37820
2.64410
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2.51076
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2.38862
•43932
2.27626
44
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2.64177
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2.50864
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2.38668
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2.27447
45
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2.63945
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2.50652
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2.38473
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2.27267
46
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2.63714
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2.50440
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2.38279
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2.27088
47
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2.63483
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2.50229
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2.38084
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2.26909
48
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2.63252
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2.50018
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2.37891
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2.26730
49
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2.63021
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2.49807
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2.37697
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2.26552
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2.62791
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2.49597
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2.26374
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2.62561
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2.49386
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2.37311
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2.26196
52
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2.62332
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2.49177
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2.37118
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2.26018
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2.62103
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2.48967
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2.36925
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2.25840
54
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2.61874
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2.48758
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2.36733
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2.25663
55
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2.61646
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2.48549
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2.36541
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2.25486
56
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2.61418
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2.48340
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2.36349
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2.25309
57
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2.61190
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2.48132
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2.36158
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2.25132
58
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2.60963
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2.47924
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2.35967
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2.24956
59
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NATURAL TANGENTS AND CO-TANGENTS 535
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2.24604
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2.05030
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1.96261
60
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2.14288
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2.04879
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1. 96 1 20
59
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2.24252
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2.24077
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2.23902
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2.13801
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1.95277
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2-13154
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2.03825
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2.22683
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2.12671
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2.03376
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1.94718
49
12
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2.12511
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2.12350
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2.03078
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2.12190
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46
15
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2.12030
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2.02780
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1.94162
45
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2.21819
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2.11871
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2.02631
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1.94023
44
17
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2.21647
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2.11711
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2.02483
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1.93885
43
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2.21475
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2.11552
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2.02335
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1.93746
42
19
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2.21304
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2.II392
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2.02187
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1.93608
41
20
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2.21132
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2.II233
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2.02039
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1.93470
40
21
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2.20961
•47377
2.11075
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2.01891
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1.93332
39
22
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2.20790
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2.10916
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2.01743
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1.93195
38
23
•45327
2.20619
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2.10758
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2.01596
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1.93057
37
24
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2.20449
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2.10600
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2.01449
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1.92920
36
25
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2.20278
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2.10442
•49677
2.01302
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1.92782
35
26
•45432
2.20108
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2.10284
•49713
2.01155
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1.9264s
34
27
•45467
2.19938
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2.10126
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2.01008
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1.92508
33
28
•45502
2.19769
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2.09969
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2.00862
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1.92371
32
29
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2.19599
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2.0981 1
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1.9223s
31
30
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2.19430
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2.09654
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2.00569
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1.92098
30
31
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2.19261
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2.09498
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2.00423
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1. 91962
29
32
•45643
2.19092
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2.09341
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2.00277
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1.91826
28
33
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2.18923
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2.09184
•49967
2.OOI3I
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1. 9 1 690
27
34
•45713
2.18755
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2.09028
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1.99986
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1.91554
26
35
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2.18587
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2.08872
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1. 99841
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1.91418
25
36
•45784
2.18419
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2.08716
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1.99695
•52279
1. 91 282
24
37
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2.18251
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2.08560
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1.99550
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1.91147
23
38
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2.18084
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2.08405
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1.99406
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1.91012
22
39
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2.17916
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2.08250
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1. 99261
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1.90876
21
40
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2.17749
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2.08094
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1.99116
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1. 90741
20
41
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18
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2.07630
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1.98684
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1.90337
17
44
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2.17083
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2.07476
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16
45
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1.98396
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1 .90069
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46
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2.07167
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1.89935
14
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1. 981 10
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13
48
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12
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1.97253
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1.80000
7
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56
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1.88469
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6
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6
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536 NATURAL TANGENTS AND CO-TANGENTS
28° 1
29°
30°
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Co-TAN.
Tan. C
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Tan.
Co-TAN.
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1.66428
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80281
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1.73089
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1.66318
59
2
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1.87809
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80158
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1.72973
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1.66209
58
3
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1.72857
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1.66099
57
4
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1.87546
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1.65990
56
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1. 6588 1
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6
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79665
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1.65772
54
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1.72278
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1-65534
52
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1. 8689 1
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1.72163
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1.65445
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1.72047
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1.86630
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79051
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1.71932
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1.65228
49
12
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1.86499
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78929
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I.71817
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1.65120
48
13
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1.86369
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78807
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1.71702
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I.65011
47
14
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1.86239
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1. 7 1 588
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1.64903
46
15
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78563
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1.71473
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1.64795
45
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1.85979
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78441
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1.71358
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1.64687
44
17
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1.85850
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78319
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1.71244
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1.64579
43
i8
•53844
1.85720
■56117 1
78198
.58435
1.71129
.60801
1.64471
42
19
.53882
1-85591
■56156 I
78077
.58474
1. 71015
.60841
1.64363
41
20
•53920
1.85462
■56194 1
77955
.58513
1.70901
.60881
1.64256
40
21
•53957
I-85333'
■56232 I
77834
.58552
1.70787
.60921
1. 641 48
39
22
•53995
1.85204
.56270 I
77713
.58591
1.70673
.60960
1. 6404 1
38
23
•54032
1.85075
.56309 1
77592
.58631
1.70560
.61000
1.63934
37
24
.54070
1.84946
•56347 1
77471
.58670
1.70446
.61040
1.63826
36
25
•54107
1. 84818
.56385 I
77351
.58709
1^70332
.61080
I.63719
35
26
.54145
1.846S9
.56424 I
77230
.5S748
1. 70219
.61120
1. 636 1 2
34
27
■54183
1.84561
.56462 1
77110
.58787
1.70106
.61160
1.63505
33
28
.54220
1.84433
■56500 I
76990
.58826
1.69992
.61200
1.63398
32
29
•54258
1.84305
.56539 I
76869
.58865
1.69879
.61240
1.63292
31
30
.54296
1.84177
.56577 1
76749
.58904
1.69766
.61280
I.63185
30
31
•54333
1.84049
.56616 1
76630
.58944
1.69653
.61320
1.63079
29
32
•54371
1.83922
.56654 1
76510
.58983
1.69541
.61360
1.62972
28
33
•54409
1.83794
.56693 I
76390
.59022
1.69428
.61400
1.62866
27
34
•54446
1.83667
.56731 1
76271
.59061
1.69316
.61440
1.62760
26
35
.54484
1.83540
.56769 1
76151
.59101
1.69203
.61480
1.62654
25
36
•54522
1.83413
.56808 I
76032
.59140
1.69091
.61520
1.62548
24
37
•54560
1.83286
.56846 I
75913
.59179
1.68979
.61561
1.62442
23
38
•54597
1.83159
■56885 I
75794
.59218
1.68866
.61601
1.62336
22
39
•54635
1.83033
.56923 I
75675
.59258
i^68754
.61641
1.62230
21
40
•54673
1.82906
.56962 I
75556
.59297
1.68643
.61681
1.62125
20
41
•547 I I
1.82780
.57000 I
75437
.59336
I ■68531
.61721
1.62019
'?
42
•54748
1.82654
•57030 I
75319
.59376
1.68419
.61761
1.61914
18
43
.54786
1.82528
.57078 I
75200
.59415
1.68308
.61801
1.61808
17
44
.54824
1.82402
.57116 1
75082
.59454
1.681Q6
.61842
1.61703
16
45
.54862
1.82276
.57155 1
74964
.59494
1.68085
.61882
1.61598
IS
46
■54900
1. 82 1 50
.57193 1
74846
•59533
1.67974
.61922
1-61493
14
47
•54938
1.82025
.57232 I
74728
.59573
1.67863
.61962
1. 6 1 388
13
48
■54975
1.81899
.57271 I
74610
.59612
1.67752
.62003
1.61283
12
49
•55013
1.81774
.57309 I
74492
■59651
1.67641
■62043
1.61179
II
50
•55051
1.81649
.57348 1
74375
•59691
1.67530
.62083
1.61074
10
51
•5508Q
1.81524
.57386 I
74257
•59730
1.67419
.62124
1.60970
9
52
•55127
1. 8 1 399
.57425 1
74140
•59770
1.67309
.62164
1.60865
8
53
•5516s
1.81274
.57464 1
74022
•59809
1.67198
.62204
1. 60761
7
54
•55203
1. 81 150
.5:503 1
73905
.59849
1.67088
.62245
1.60657
6
55
•55241
1.81025
.57541 1
73788
.59888
1.66978
.62285
1-60553
5
56
•55279
1. 8090 1
.57580 I
73671
.59928
1.66867
■62325
1.60449
4
57
•55317
1.80777
•57619 I
73555
.59967
1.66757
.62366
1.6034s
3
58
•55355
1.80653
.57657 1
73438
.60007
1.66647
.62406
1. 60241
2
59
•55393
1-80529
.57696 I
73321
.60046
1.66538
.62446
1.60137
I
60
•55431
1 .80405
•57735 1
7320s
.60086
1.66428
62487
1.60033
0
Co-TAN.
Tan.
Co-TAN.
Tan.
Co-TAN.
Tan.
Co-TAN.
Tan.
6
1«
60°
5
9°
1 5
8°
NATURAL TANGENTS AND CO-TANGENTS 537
32°
1 33°
34°
35°
/
Tan.
Co-TAN.
Tan.
Co-TAN.
Tan.
Co-TAN.
Tan. C
O-TAN.
'
o
.62487
1.60033
-64941
1-53986
.67451
1.48256
.70021 1
42815
60
I
.62527
I -59930
.64982
1.53888
•67493
1.48163
.70064 I
42726
59
2
.62568
1.59826
-65023
I-5379I
.67536
1.48070
.70107 1
42638
58
3
.62608
1-5972.^
-65065
1-53693
.67578
1^47077
.70151 1
42550
57
4
.62649
1.59620
.65106
1-53595
.67620
1-47885
.70104 I
42462
56
5
.6268g
1-59517
-65148
1-53497
.67663
1-47702
.70238 1
42374
55
6
.62730
1.59414
-65189
I -53400
.67705
1.47600
.70281 I
42286
54
7
.62770
1-59311
•65231
I -53302
•67748
1.47607
•70325 1
42108
53
8
.62811
1.59208
■65272
1-53205
•67790
1-47514
.70368 1
43I10
52
Q
.62852
1.59105
-65314
1-53107
.67832
1.47422
.70412 1
42022
51
lO
.62892
1.59002
-65355
1.53010
•67S75
1.47330
•70455 1
41934
50
11
•62933
1.58900
-65397
1-52913
•67917
1.47238
.70409 I
41847
49
12
.62973
1.58797
-65438
1.52816
.67960
1.47146
.70542 1
41759
48
13
.63014
1-58695
.65480
1.52719
.68002
1.47053
.70586 1
41672
47
14
■63055
1-58593
-65521
1.52622
.68045
1.46062
.70620 1
41584
46
15
•63095
1.58490
-65563
1-52525
.68088
1.46870
•70673 1
41497
45
i6
.63136
1.58388
.65604
1.52429
.68130
1.46778
.70717 1
41409
44
17
•63177
1.58286
.65646
1-52332
•68173
1.46686
.70760 1
41322
43
i8
.63217
1.58184
.65688
1-52235
.68215
1.46505
.70804 1
41235
42
19
•63258
1.58083
.65729
1-52139
.68258
1.46503
.70848 1
41148
41
20
.63299
1.57981
.65771
1-52043
.68301
1. 464 11
.70891 I
41061
40
21
•63340
1.57879
.65813
1.51946
•68343
1.46320
•70035 1
40974
39
22
•63380
1.57778
.65854
1.51850
.68386
1.46220
.70070 1
40887
38
23
.63421
1.57676
.65896
1.51754
.68429
1-46137
.71023 I
40800
37
24
.63462
1.57575
.65938
1.51658
.68471
1 .46046
.71066 1
40714
36
25
•63503
1.57474
.65980
1.51562
.68514
1-45055
.71110 1
40627
35
26
•63544
1.57372
.66021
1.51466
.68557
1.45864
.71154 1
40540
34
27
•63584
1.57271
.66063
1. 5 1 370
•.68600
1.45773
.71108 1
40454
33
28
.63625
1.57170
.66105
1.51275
.68642
1.45682
.71242 1
40367
32
29
.63666
1-57069
.66147
1.51179
.68685
1.45502
.71285 1
40281
31
30
.63707
1-56969
.66189
1.51084
.68728
1.45501
.71329 1
4019s
30
31
.63748
1.56868
.66230
1.50988
.68771
1.45410
.71373 1
40100
29
32
.63789
1.56767
.66272
1.50893
.68814
1.45320
.71417 1
40022
28
33
.63830
1.56667
-66314
1.50797
.68857
1.45220
.71461 1
30036
27
34
.63371
1.56566
.663 S6
1.50702
.68000
1.45130
.71505 1
30850
26
35
.63912
1 .56466
.66398
1.50607
.68042
1.45040
.71540 1
30764
25
36
•63953
1.56366
.66440
1.50512
.68085
1.44058
.71593 1
30670
24
37
.63094
1.56265
.66482
1.50417
.60028
1.44868
•71637 I
30503
23
38
•64035
1.56165
.66524
1.50322
.69071
1.44778
.71681 1
30507
22
39
.64076
1.56065
.66566
1.50228
.69114
1.44688
.71725 I
30421
21
40
.64117
1.55966
.66608
1^50133
.69157
1.44508
•71769 I
30336
20
41
.64158
1.55866
.66650
1.50038
.69200
1.44508
.71813 1
39250
19
42
.64199
1.55766
•66692
1.49944
.60243
1.44418
.71857 1
39165
18
43
.64240
1.55666
-66734
1.49849
.60286
1.44329
.71901 1
39079
17
44
.64281
i.55-=567
.66776
1.49755
■60320
1.44230
.71046 I
38994
16
45
.64322
1-55467
.66818
1.40661
.60372
1.44140
.71000 I
38909
15
46
•64363
1.55368
.66860
1.49566
.60416
1.44060
•72034 I
38824
14
47
.64404
1.55269 !
.66902
1.49472
-60450
1.43070
.72078 1
38738
13
48
.64446
1.55170
.66944
1-49378
.60502
1. 43881
.72122 1
38653
12
49
.64487
1.55071
.66986
1.40284
-60545
1.43702
.72166 I
38568
11
50
•64528
1.54972
.67028
1.49190
.60588
1.43703
.72211 I
38484
10
51
.64569
1.54873
.67071
1-49097
.60631
1.43614
•72255 I
38399
9
52
.64610
1-54774
.67113
1.49003
.60675
1.43525
.72200 1
38314
8
53
.64652
1-54675
•67155
1.48909
.60718
1.43436
•72344 1
38220
7
54
•64693
1-54576
.67197
1.48816
.60761
1.43347
.72388 1
38145
6
55
•64734
1.54478
■67230
1.48722
.60804
1.43258
.72432 1
38060
5
56
•64775
1-54379
.67282
1.48620
.60847
1.43160
•72477 1
37076
4
57
.64817
1.54281
-67324
1.48536
.60801
1 .43080
-72521 1
37801
3
58
.64858
1-54183
.67366
1.48442
•60034
1.42002
.72565 I
37807
2
59
.64899
1.54085
.67409
1.48349
■69077
1.42003
.72610 1
37722
1
60
.64941
1-53986
•67451
1.48256
.70021
1.42815
.72054 1
37638
0
f
Co-TAN.
Tan.
Co-TAN.
Tan.
Co-TAN.
Tan.
Co-TAN.
Tan.
/
5
70 •
5
Q°
5
5°
54°
538 NATURAL TANGENTS AND CO-TANGENTS
36°
Tan. Co-tan.
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
.72654
.72699
•72743
.72788
.72832
.72877
.72921
.72966
.73010
.73055
.73100
•73144
.73189
•73234
.73278
•73323
.73368
•73413
•73457
•73502
.73547
•73592
.73637
.73681
■73726
.73771
•73816
•73861
•73906
•73951
•73996
.74041
.74086
•74131
.74176
.74221
.74267
•74312
•74357
.74402
.74447
.74492
.74538
• 74583
.74628
•74674
•747T9
■74764
.74S10
•74855
•74900
.74946
•74991
•75037
.75082
•75128
•75T73
•75219
.75264
•75310
.75355
37°
Tan. Co-tan.
1.37638
1-37554
1.37470
1-37386
1.37302
1.37218
1-37134
1.37050
1.36967
1.36883
1 .36800
1.36716
1.36633
1.36549
1.36466
1-36383
1 -36300
1.36217
1-36133
1.36051
1-35968
1-35885
1.35802
[-35719
f -35637
1-35554
1-35472
I -35389
1-35307
1-35224
1-35142
1.35060
1.34978
1 -34896
1.34814
1.34732
1-34650
1.34568
1.34487
I -34405
1-34323
1.34242
1-34160
1-34079
1-33998
1-33916
1-33835
1-33754
1-33673
1-33592
I-335II
1-33430
1-33349
1.33268
1-33187
1-33107
1.33026
1.32946
1.32865
1.32785
1.32704
Co-TAN. Tan.
53^
75355
75401
75447
75492
75538
75584
75629
75675
75721
75767
.75812
.75858
.75904
•75950
•75996
.76042
.76088
.76134
.76180
,76226
.76272
.76318
.76364
.76410
.76456
.76502
.76548
.76594
.76640
.76686
-76733
.76779
.76825
.79871
.76918
.76964
.77010
•77057
.77103
.77149
-77196
.77242
-77289
.77335
-77382
.77428
•77475
•77521
.77568
.77615
.77661
.77708
.77754
.77801
.77848
•77895
•77941
.77988
.78035
.78082
.78129
38=
Tan. Co-tan.
1.32704
1.32624
1-32544
1-32464
1.32384
1-32304
1.32224
1-32144
1.32064
1.31984
1-31904
1.31825
1.31745
1.31666
1. 3 1 586
1-31507
1-31427
1.31348
1.31269
1.31190
1.31110
1.31031
1.30952
1.30873
1.30795
1.30716
1.30637
1-30558
1.30480
1.30401
1.30323
1.30244
1. 30 1 66
1.30087
1 .30009
1-29931
1-29853
1.29775
1.29696
1.29618
1-29541
1.29463
1.29385
1.29307
1.29229
1.29152
1.29074
1.28997
1.28919
1.28842
1.28764
1.28687
1.28610
1-28533
1.28456
1.28379
1.28302
1.2822s
1.28148
1.28071
1.27994
.78129
.78175
.78222
.78269
.78316
•78363
.78410
•78457
.78504
•78551
.78598
.78645
.78692
.78739
.78786
•78834
.78881
.78928
.78975
.79022
.79070
•79117
•79164
.79212
•79259
•79306
•79354
.79401
• 79449
•79496
•79544
•79591
•79639
.79686
.797.34
.79781
.79820
.79877
.79924
.79972
.80020
.80067
.80115
.80163
.80211
.80258
.80306
•80354
.80402
.80450
.80498
.80546
-80594
.80642
.80690
.80738
.80786
.808^4
.80882
.80930
.80978
CO'TAn.I Tan.
52°
39°
Tan. Co-tan,
1.27994
1. 27917
1.27841
1.27764
1.27688
1.27611
1.27535
1.27458
1.27382
1.27306
1.27230
1-27153
1-27077
1. 27001
1.26925
1.26849
1.26774
1.26698
1.26622
1.26546
1.26471
1-26395
1.26319
1.26244
1.26169
1.26093
1.26018
1-25943
1-25867
1-25792
1-25717
1.25642
1.25567
1.25492
1.25417
1.25343
1.25268
1.25193
1.25118
1.25044
1.24969
1.24895
1.24820
1.24746
1.24672
1.24597
1.24523
1.24449
1.24375
1.24301
1.24227
1.24153
1.24079
1.24005
1-23931
1-23858
1-23784
1-23710
1-23637
1-23563
1.23490
Co-TAN. Tan.
51°
.80978
.81027
.81075
.81123
.81171
.81220
.81268
.81316
.81364
.81413
.81461
.81510
.81558
.81606
.81655
.81703
.81752
.81800
.81849
.81898
.81946
.81995
.82044
.82092
.82141
.82190
.82238
.82287
.82336
.82385
.82434
.82483
.82531
.82580
.82629
,82678
,82727
.82776
.82825
.82874
.82923
.82972
.83022
.83071
.83120
.83169
.83218
.83268
-83317
-83366
.83415
-83465
-83514
-83564
-83613
.8^662
.83712
.83761
.8^811
.83860
-83910
Co-TAN. Tan
50°
NATURAL TANGENTS AND CO-TANGENTS 539
40° I
41° I
42°
43°
o
Tan.
Co-tan.
Tan.
Co-tan.
Tan.
Co-tan.
Tan.
Co-TAN.
/
.83010
I.I0175
.86929
1.1.5037
.90040
1.11061 1
•932*a
1.07237
60
I
.83960
i^i9io5
.86980
1. 1 4969
.90093
1.10996
•93306
1.07174
59
2
.84009
I. 19035
.87031
1.14902
.90146
1.10931
•93360
1. 07 1 12
58
3
.84050
1.18964
.870S2
1. 14834
.90199
1.10867
•93415
1.07049
57
4
.84108
1.18894
•87133
1.14767
.90251
1.19802
•93469
1.06987
56
c
.84158
1.18824
.87184
1.14699
.90304
1^10737
•93524
1.06925
55
6
.84208
1.18754
•87236
1.14632
•9'o357
1^10672
•93578
1.06862
54
J
.84258
1.18684
.872S7
1.1456s
.90410
1.10607
•93633
1 .06800
53
8
.84307
1.18614
•87338
I. I 4498
.90463
i^io543 i
.93688
1.06738
52
g
•84357
1.18544
.87389
1.14430
.00516
I. 10478
-93742
1.06676
51*
lO
.84407
1.18474
.87441
1-14363
.90569
I. 10414
•93797
X. 066 1 3
50
11
•84457
1.18404
.87492
1.14296
.90621
1.10349 ]
•93852
1-06551
49
12
.84507
1.18334
•87543
I. 14229
.90674
1.10285 '
•93906
1.06489
48
13
.84556
1.18264
•87595
1.14162
•90727
1.10220
•93961
1.06427
47
14
.84606
I. 18194 1
.87646
1.14095
.90781
1.10156
.94016
1.06365
46
!■;
.84656
1.18125
.87698
1.14028
■90834
1. 10091
.94071
1.06303
45
16
.84706
1.18055
■S7749
1.13961
.90887
1.10027
.94125
I.06241
44
17
.84756
1.179S6 1
.87801
1.13894
.90940
1.09963
.94180
1. 06 1 79
43
18 .84806
I. 17916 ;
.87852
1.13828
.90993
1.09899
•94235
1. 061 17
42
19
.84856
I. 17846 ,
.87904
1.13761 i
.91046
1.09834
.94290
1.06056
41
20
.84906
I. 17777
•87955
1.13694
.91099
1.09770
•94345
1.05994
40
2t
•84956
1-17708
.88007
1. 13627
•91153
1.09706
.94400
1-05932
39
22
.85006
I.I7638
.88059
1.13561
.91206
1.09642
•94455
1.05870
38
23
•85057
I.I7569
.88110
1.13494
.91259
1.09578
-94510
1.05809
37
24
.85107
I.I7SOO
.881&2
1.13428
•91313
1.09514
•94565
I-05747
36
25
•85157
1. 17430
.88214
1-13361
.91366
1.09450
.94620
1.05685
35
26
.85207
1-17.361
.88265
1.13295
.01419
1.09386
.94676
1.05624
34
27
•85257
1. 17292
•88317
1. 13228
•91473
1.09322 ,
-94731
1.05562
33
28
.85307
1. 17223
.88369
I. 13162
.91526
1.09258
.94786
1.05501
32
29
•85358
1-17154
.88421
1.13096
.91580
1-09195
.94841
I -05439
31
30
.85408
I-17085 1
.88473
I. 13029
-91633
1.09131
.94896
1.05378
30
31
.85458
1. 17016 j
.88524
1. 1 2963
.91687
1.09067
•94952
1.05317
29
32
•85509
1.16947
•88576
1.12897
.91740
1.09003
.95007
1-05255
28
33
•85559
1.16878
.88628
1.12831
.91794
1 .08940
.95062
1-05194
27
34
.85609
1.16809 1
.88680
1.12765
.91847
1.08876
.95118
I -05 1 33
26
35
.85660
I. 16741
•88732
1.12699
.^1901
1.08813
•95173
1.05072
25
36
•85710
1.16672
.88 784
1. 12633
-91955
1.08749
.95229
1.05010
24
37
.85761
1.16603
.88836
I. 12567
.92008
1.08686
.95284
1.04949
23
38
.85811
1.16535
.88888
I. 12501
.92062
1.08622
•95340
1.04888
22
39
.85862
1.16466
.88040
1-12435
.92116
1.08559
•95395
1.04827
21
40
.85912
1. 16398 1
.88992
1. 12369
.92170
1 .08496
•95451
1.04766
20
41
•85963
1. 16320 '
•89045
1.12303
.92224
1.08432
•95.506
1.04705
19
42
.86014
1. 16261
.89097
1.12238
.92277
1.08369
■95562
1 .04644
18
43
.86064
1.16192 '
.89149
1.12172
-92331
.1.08306
.95618
1.04583
17
44
.86115
1.16124
.89201
I. 12106
-92385
1.08243
•95673
1.04522
16
45
.86166
i.i6o;6
.89253
I. 12041
.92439
1.08179
■95729
1. 0446 1
IS
46
.86216
1.15987
.89306
1.11975
-92493
1.08116
■95785
1. 0440 1
14
47
.86267
1.15919
-89358
1. 11909
•92547
1 .08053
.95841
1.04340
13
48
.86318
1.15851
.89410
1.11844
.92601
1.07990
•95897
1.04279
12
49
.86368
1-15783
.89463
1.11778
.92655
1.07927
•95952
1. 042 18
1 1
50
.86419
i-i57r5
•89515
1.11713
-92709
1.07864
.96008
1.04158
10
51
.86470
1. 15647
•89567
1. 11648
.92763
ix>78oi
.96064
1.04097
9
52
.86521
1-15579
.89620
1.11582
.92817
1.07738
.96120
1 .04036
8
53
.86572
I-15511
.89672
1.11517
.02872
1.07676
.96176
1.03976
7
54
.86623
1-15443
.89725
1.11452
.92926
1.07613
.96232
1.03015
6
55
.86674
1-15375
•80777
1.11387
.92980
1.07550
.96288
1-03855
5
56
•86725
1.15308
.80830
1.11321
•93034
1.07487
•96344
1.03794
4
57
.86776
1. 15240
.80883
1.11256
.93088
1.07425
.96400
1.03734
3
58
.86827
1.15172
.8903=;
1.11191
•93 1 43
1.07362
-96457
1.03674
2
59
.86878
1. 15104
.89988
T.11126
•93197
1.07299
.96513
1.03613
I
60
.86929
1-1S037
.90040
1.11061
■93252
1.07237
.96569
1.03553
0
'
Co-tan
4
Tan.
9°
Co-tan.
4
Tan.
8°
Co-tan.
4
Tan.
70
Co-TAN
4
Tan.
6"^
/
540 NATURAL TANGENTS AND CO-TANGENTS
44°
440
44°
/
Tan.
Co-TAN.
/
'
Tan.
Co-TAN.
/
' Tan.
Co-TAN.
»
o
.96569
i^03553
60
21
•97756
1.02295
"^
41
98901
1.01112
19
I
.96625
I -03493
59
22
-97813
1.02236
38
42
98958
I-OIO53
18
2
.96681
I -03433
58
23
.97870
1.02176
37
43
99016
1.00994
17
3
.96738
1-03372
57
24
.97927
1.02117
36
44
99073
1.00935
16
4
•96794
1-03312
56
25
-97984
1.02057
35
45
99I3I
1.00876
15
5
.96850
1-03252
55
26
.98041
1.01998
34
46
99189
1.00818
14
6
.96907
1.03192
54
27
.98098
1. 01 939
33
47
99247
1.00759
13
7
•96963
1-03132
53
28
-98155
1.01879
32
48
99304
1.00701
12
8
.97020
1. 03072
52
29
.98213
1.01820
31
49
99362
1.00642
II
9
.97076
1. 030 1 2
51
30
.98270
1.01761
30
50
99420
1.00583
10
lo
•97133
1.02952
50
31
.98327
1. 01 702
29
51
99478
1.00525
9
II
•97189
1.02892
49
32
-98384
1.01642
28
52
99536
1.00467
8
12
.97246
1.02832
48
33
.98441
1.01583
27
53
99594
1 .00408
7
13
•97302
1.02772
47
34
.98499
1.01524
26
54
99652
1.00350
6
14
•97359
1.02713
46
35
-98556
1. 01 465
25
55
99710
1.00291
S
15
.97416
1.02653
45
36
-98613
1.01406
24
56
99768
1.00233
4
i6
•97472
1 02593
44
37
.9S671
1.01347
23
57
99826
1.00175
3
17
•97529
1^02533
43
38
.98728
1.01288
22
58
99S84
1.00116
2
i8
•97586
1.02474
42
39
.98786
I.01229
21
59
99942
1.00058
1
19
•97643
1.02414
41
40
•98843
I.OI170
20
60 I
I
0
20
.97700
1-0235S
40
f
CO-TAN.
Tan.
/
»
Co-TAN.
Tan.
/
' Co-TAN.
Tan.
"T
4
5°
4
5°
45°
NATURAL SINES AND COSINES
'
(
Sine
0
.00000
1
.00029
2
.00058
3
.00087
4
.00116
5
•00145
6
.00175
7
.00204
8
•00233
9
.00262
10
.00291
11
.00320
12
•00349
13
.00378
14
.00407
15
.00436
16
.00465
17
•00495
18
.00524
IQ
.00553
20
.00582
'
Cosine
8
0°
0°
0°
Cosine
/
/
Sine
Cosine
'
Sine
Cosine
t
60
^
.00611
.99998
39
41
.01193
•99993
19
59
22
.00640
99998
38
42
.01222
•99993
18
58
23
.00669
99998
37
43
.01251
•99992
17
57
24
.00698
9999S
36
44
.01280
.99992
16
56
25
.00727
99997
35
45
.01309
.99991
IS
55
26
.00756
99997
34
46
.01338
.99991
14
54
27
.00785
99997
33
47
.01367
.99991
13
53
28
.00814
99997
32
48
.01396
•99990
12
52
29
.00844
99996
31
49
•01425
.99990
II
51
30
.00873
99996
30
50
•01454
•99989
10
50
31
.00902
99996
29
51
•01483
•99989
9
.99999
49
32
.00931
99996
28
52
•01513
.99989
8
.99999
48
33
.00960
99995
27
53
.01542
.99988
7
■99999
47
34
.00989
99995
26
54
•01571
.99988
6
■99999
46
35
.01018
99995
25
55
.01600
.99987
5
•99999
45
36
.01047
99995
24
56
.01629
.99987
4
.99999
44
37
.01076
99994
23
57
.oi6=;8
.99986
3
.99999
43
38
.01105
99994
22
58
.01687
.99986
2
-99999
42
39
.01134
99994
21
59
.01716
•99985
I
.99998
41
40
.01164
99993
20
60
•01745
•99985
0
.99998
40
Sine
»
/
Cosine
Sine
/
/
Cosine
Sine
T
59°
8
9'
)
8<
r
NATURAL SINES AND COSINES
541
1 1
0
2°
3°
40
Sine
Cosine
Sine (
:osine
Sine (
:OSINE
Sine (
I^OSINE
*
•01745
.99985
.03490
99939
•05234
99863
;o6976
99756
60
•01774
.90984
•03519
99938
•05263
99861
.07005
99754
59
.01803
.99984
.03548
99937
.05292
99860
.07034
99752
58
.01832
.99983
.03577
99936
.05321
99858
.07063
99750
57
.01862
•99083
.03606
99935
•05350
99857
.07092
99748
56
.01891
.99982
■0363s
99934
•05379
99855
.07121
99746
55
.01920
.99982
.03664
99933
.05408
99854
.07150
99744
54
.01949
.99981
.03693
99932
.05437
99852
.07179
00742
53
.01978
.99980
•03723
99931
.05466
99851
.07208
99740
52
.02007
.99980
•03752
99930.
•05495
99849
•07237
09738^
51
.02036
.99979
•03781
99929
•05524
99S47
.07266
99736
50
.02065
.99979
.03810
99027
•05553
99846
.07295
99734
49
.02094
.99978
•03839.
99926
•05582
99844
.07324
90731
48
.02123
•99977
.03868
99025
.05611
99842
.07353
99729
47
.021 =;2
•90977
.03897
99924
.05640
99841
.07382
99727
46
.o2t8i
.99976
.03926
99923
.05669
99839
.07411
99725
45
.022TI
.99976
.03955
90922
.05698
99838
.07440
99723
44
.02240
■99975
.03984
99921
•05727
99836
.07469
90721
43
.02269
.99974
.04013
99919
.05756
99834
.0749S
99719
42
.02298
•90974
.04042
99918
.05785
90833
.07527
99716
41
.02327
•99973
.04071
99917
.05814
99831
.07556
99714
40
•02356
.90972
.04100
99916
.05844
99820
.07585
99712
30
•02385
.99972
.04129
99915
•05873
99827
.07614
99710
38
.02414
•99971
.04159
99913
.05902
99826
.07643
99708
37
.02443
•99970
.04188
99912
.05931
99824
.07672
99705
36
.02472
•99969
.04217
999 II
.05960
99822
.07701
99703
35
.02501
.99969
.04246
99910
.05989
99821
•07730
99701
34
.02530
.99968
.04275
99909
.06018
99819
•07759
99699
33
.02560
•99967
.04304
99907
.06047
99817
.07788
99696
32
•02589
.99966
•04333
99906
.06076
99815
.07817
99694
31
.02618
.99966
.04362
99905
.06105
99813
.07846
99692
30
.02647
•99965
•04391
99904
.06134
99812
.07S75
99689
29
.02676
•99964
.04420
99902
.06163
99810
.07904
99687
28
.02705
•99963
.04449
99901
.06192
99808
•07933
99685
27
•02734
•99963
.04478
99900
.06221
99806
.07962
99683
26
.02763
.99962
.04507
99898
.06250
99804
•07991
99680
25
.02792
.99961
•04536
99897
.06279
99803
.08020
99678
24
.02821
.99960
•04565
99896
.06308
99801
.08049
99676
23
.02850
•99959
•04594
99894
■06337
99799
.08078
99673
22
.02879
.999-9
.04623
99893
.06366
99797
.08107
99671
21
.02908
.99958
.04653
99892
.06395
99795
.0S136
99668
20
.02938
•99957
.04682
99890
.06424
99793
.08165
99666
19
.02967
•99956
.04711
99SS9
.06453
99792
.08194
99664
18
.02996
•99955
.04740
99888
.06482
99790
.08223
99661
17
.03025
•99954
.04769
99886
.06511
99788
.082 S2
99659
16
•03054
•99953
.04798
99885
.06540
99786
.08281
90657
15
.03083
•99952
.04827
99883
.06560
99784
.08310
00654
14
.03112
•99952
.04856
90882
.06=; 98
99782
•08339
90652
13
.03141
•99951
.04885
99881
.06627
99780
.08368
99649
12
.03170
.99950
.04914
99879
.06656
99778
•08397
99647
II
.03199
•99949
.04943
99878
.06685
99776
.08426
99644
10
.03228
•99948
.04972
99876
.06714
99774
•08455
99642
9
•03257
•90947
.05001
99875
.06743
99772
.08484
99639
8
.03286
•99946
.05030
99873
.06773
99770
•08513
99637
7
.03316
•99945
.05059
99872
.06802
90768
.08542
99635
6
•03345
.99944
.05088
99870
.06831
99766
.08 1;?!
99632
5
.03374
•99943
.05117
99869
.06860
99764
.08600
99630
4
•03403
.99942
.05146
99867
.06889
99762
.08629
99627
3
•03432
•99941
•05175
99866
.06918
99760
.08658
99625
2
.03461
•99940
.05205
99864
.06047
99758
.08687
90622
I
.03490
•09039
•05234
99863
.06976
99756
.08716
99619
0
Cosine
Sine
Cosine
Sine
Cosine
Sine
Cosine
Sine
t
88
0
87°
86°
85«
542
NATURAL SINES AND COSINES
5^
6°
70
I
8
0
/
Sine
Cosine
Sine (
:osine
Sine (
:0SINE
Sine
Cosine
/
o
.08716
.99619
•10453
99452
.12187
99255
.13917
.99027
60
I
.08745
.99617
.10482
99449
.12216
99251
.13946
.99023
59
2
.08774
.99614
.10511
99446
.12245
99248
.13975
.99019
58
3
.08803
.99612
.10540
99443
.12274
99244
.14004
•99015
57
4
•°fo^'
.99609
.10569
99440
.12302
99240
.14033
.99011
56
5
.08860
.99607
•10597
99437
.12331
99237
.14061
.99006
55
6
.088S9
.99604
.10626
99434
.12360
99233
.14090
.99002
54
7
.08918
.99602
.10655
99431
.12389
99230
.14119
.98998
53
8
.08947
•99599
.10684
99428
.12418
99226
.14148
•98994
52
9
.08976
.99596
.10713
99424
.12447
99222
.14177
.98990
51
lo
.09005
•99594
.10742
99421
.12476
99219
.14205
.98986
50
11
.09034
•99591
.10771
99418
.12504
•99215
.14234
.98982
49
12
.09063
.99588
- .10800
99415
.12533
.99211
.14263
.98978
48
13
.09092
.99586
.10829
99412
.12562
.99208
.14292
•98973
47
14
.09121
•99583
.io8s8
99409
.12591
.99204
•14320
.98969
46
15
.09150
.99580
.10887
99406
.12620
.99200
.14349
.98965
45
i6
.09179
•99578
.10916
99402
.12649
99197
.14378
.98961
44
17
.09208
•99575
.10945
99399
.12678
•99193
.14407
•98957
43
i8
.09237
•99572
.10973
99396
.12706
.99189
.14436
•98953
42
19
.09266
•99570
.11002
99393
.12735
.99186
.14464
.98948
41
20
.09295
•99567
.11031
99390
.12764
.99182
.14493
.98944
40
21
.09324
•99564
.11060
99386
.12793
.99178
.14522
.98940
39
22
•09353
.99562
.11089
99383
.12822
•99175
•14551
.98936
38
23
.09382
•99559
.11118
99380
.12851
.99171
.14580
.98931
37
24
.09411
•99556
.11147
99377
.12880
•99167
.14608
•98927
36
25
.09440
•99553
.11176
99374
.12908
99163
.14637
.98923
35
26
.09469
•99551
.11205
99370
.12937
.99160
.14666
.98919
34
27
.09498
.99548
.11234
99367
.12966
•99156
.14695
.98914
33
28
•09527
•99545
.11263
99364
.12995
99152
•14723
.98910
32
29
•09556
•99542
.11291
99360
.13024
99148
.14752
.98906
31
30
•09585
•99540
.11320
99357
.13053
99144
.14781
.98902
30
31
.09614
•99537
.11349
99354
.13081
99I4I
.14810
.98897
29
32
.09642
•99534
.11378
99351
.13110
99137
.14838
.98893
28
33
.09671
•99531
.11407
99347
.13139
99133
.14867
.98889
27
34
.09700
•99528
.11436
99344
.13168
99129
.14896
.98884
26
35
.09729
.99526
.11465
99341
•I3I97
99125
.14925
.98880
25
36
.09758
•99523
.11494
99337
.13226
99122
.14954
.98876
24
37
.09787
•99520
.11523
99334
.13254
99118
.14982
.98871
23
38
.09816
•99517
.11552
99331
•13283
99114
.15011
.98867
22
39
.09845
•99514
.11580
99327
-13312
99110
.15040
.98863
21
40
.09874
•995 n
.11609
99324
.13341
99106
.15069
.98858
20
41
.09903
•99508
.11638
99320
.13370
99102
.15097
.98854
19
•42
•09932
•99506
.11667
99317
•13399
99098
.15126
.98849
18
43
.09961
•99503
.11696
99314
.13427
99094
.15155
.98845
17
44
.09990
•99500
.11725
99310
.13456
99091
.15184.
.98841
16
45
.10019
•99497
.11754
99307
.134S5
99087
,15212
.98836
15
46
.10048
•99494
.11783
99303
.13514
99083
.15241
■98832
14
47
.10077
.99491
.11812
99300
.13543
99079
.15270
.98827
13
48
.10106
.99488
.11840
99297
•13572
99075
.15299
.98823
12
49
.10135
•99485
.11869
99293
.13600
99071
•15327
.98818
11
50
.10164
.99482
.11898
99290
.13629
99067
•15356
.98814
10
51
.10192
•99479
.11927
99286
•13658
99063
.15385
.98809
9
52
.10221
•99476
.11956
99283
•13687
99059
•15414
.98805
8
53
.10250
•99473
.11985
99279
.13716
99055
.15442
.98800
7
54
.10279
.99470
.12014
99276
•13744
99051
.15471
.98796
6
55
.10308
•99467
.12043
99272
•13773
99047
.15500
•98791
5
S6
.10337
•99464
.12071
99269
.13802
99043
.15529
.98787
4
57
.10366
.99461
.12100
99265
•13831
99039
•15557
.98782
3
58
.10395
.99458
.12129
99262
.13860
99035
.15586
.98778
3
59
.10424
•99455
.12158
99258
.13889
99031
•15615
•98773
I
60
•10453
•99452
.12187
99255
•13917
99027
•15643
.98769
0
t
Cosine
Sine
Cosine
Sine
Cosine
Sine
Cosine
Sine
f
8^
[<"
83°
82°
81
0
NATURAL SINES AND
COSINES
543
9°
10°
IP
12°
*
Sine
Cosine
Sine
Cosine
Sine
Cosine
Sine
Cosine
0
.15643
.98769
.17365
.08481
.1908.
.98163
.20791
.97815
60
I
.15672
.9S764
■17393
.08476
.19109
•08157
.20820
.97809
SO
2
.15701
.98760
.17422
•08471
•1913-
•98152
.20S48
•97803
58
3
.15730
•98755
•I 745 1
.98466
.19167
.98146
.20877
•97797
57
4
.15758
.9S751
.17470
.08461
.i9ig ;
.98140
•20905
•97791
56
5
.15787
.98746
.17508
•08455
.19224
•08135
•20933
.97784
55
6
.15816
.98741
.17537
•08450
.19252
.08129
.20962
•97778
54
I 7
.15845
•98737
.17565
•98445
.19281
.98124
.20990
•97772
53
8
.15873
.98732
.17594
.0S440
•19309
.98118
.21019
■97766
52
9
.15902
.98728
.17623
■08435
•19338
.98112
.21047
•97760
SI
10
.15931
•98723
.17651
•08430
.19366
.98107
.21076
•97754
SO
II
.15950
.98718
.17680
.98425
•19395
.98101
.21104
•97748
49
12
.15088
.98714
.17708
.98420
•19423
.98096
.21132
•97742
48
13
.16017
.98709
•17737
.98414
•19452
.9S090
.21161
•97735
47
14
.16046
.98704
.17766
.98409
.19481
.98084
.21189
•97729
46
IS
.16074
.98700
.17794
.98404
.19509
.98079
.21218
.97723
45
i6
.16103
.9S695
.17823
■9S399
•19538
•08073
.21246
•97717
44
17
.16132
.98690
.17852
.98394
.19566
.98067
.21275
.97711
43
i8
.16160
.9S689
.17880
•9S389
•10505
.98061
.21303
•97705
42
19
.16189
.98681
.17909
•9S3S3
.10623
.98056
•21331
.97698
41
20
.16218
.98676
•17937
•98378
.10652
.9S050
.21360
.97692
40
21
.16246
.98671
.17966
■98373
.10680
.98044
.21388
.97686
39
22
.16275
.98667
.17905
.98368
.19709
•08030
.21477
.97680
38
.23
.16304
.986$2
.18023
.98362
•10737
•98033
.21445
•97673
37
14
•16333
.98657
.18052
■98357
.19766
.9S027
.21474
•97667
36
25
.16361
.98652
.18081
■98352
,10704
.98021
.21502
.97661
35
26
.16390
.98648
.18100
•98347
.10S23
.98016
.21530
•97655
34
27
.16419
•9S643
.18138
.98341
.19S51
.98010
.21559
.97648
33
28
.16447
.98638
.18166
■98336
.10S80
.98004
.21587
.97642
32
29
.16476
•9S633
.18105
•08331
.10008
•97997
.21616
•97636
31
30
•16505
.98629
.18224
•98325
•10037
.97992
.21644
•97630
30
31
•16533
.98624
.18252
•98320
.19965
.97987
.21672
.97623
2gf
32
.16562
.98619
.18281
•983 1 5
.19904
.97981
.21701
•97617
28
33
.16591
.98614
.18309
•9S310
.20022
■97975
.21729
.97611
27
34
.16620
.98609
.1S338
.98304
.20051
■97969
.21758
.97604
26
^J
.16648
.98604
.18367
.98299
.20079
■97963
.21786
■97508
25
36
.16677
.98600
.18305
.9S294
.20108
•97958
.21814
•07502
24
37
.16706
•98595
.18424
.98.788
.20136
•97952
.21843
■07585
23
38
•16734
.98590
'.18452
.98283
.20165
•97946
.21871
•07579
22
39
.16763
.98585
.18481
.98277
.20103
.97940
.21S99
•97573
21
40
.16792
.98580
.1S509
.9S272
.20222
.97934
.21928
•97566
20
4T
.16820
•98575
.18538
.98267
.20250
•97928
.21956
.97560
19
42
.16849
.98570
.18567
.98261
.20279
•97922
.21985
•97553
18
43
.16878
•98565
18505
.98256
.20307
•97916
.22013
■97547
17
44
.16906
•98561
.18624
.98250
.20336
.97910
.22041
•97541
16
45
.16935
•98556
.18652
.98245
.20364
•97905
.22070
•97534
15
46
.16964
•98551
.i86»i
.98240
•20393
.97899
.22098
•97528
14
*Z
.16992
.98546
.18710
■98234
.20421
•97S93
.22126
.97521
13
48
.17021
•98541
.18738
.98229
.20450
.97887
•22155
■97515
12
49
.17050
•98536
.18767
.98223
.20478
.97881
.22183
.97508
11
50
.17078
•98531
•18795
.98218
.20507
•97875
.22212
.97502
10
'si
.17107
.98526
.18824
.98212
.20535
.97860
.22240
.97496
9
52
.17136
.98521
.18S52
.98207
.26563
•07863
.22268
•97489
8
S3
.17164
•98516
.1S881
.98201
.20592
•07857
.22297
•97483
7
54
•17193
.98511
.18010
.98196
.20620
.97851
•22325
•97476
6
S5
.17222
.98506
.1S938
.98190
.20649
•97845
.22353
•07470
5
S6
.17250
.98501
.18967
.98185
.20677
•97839
.22382
•97463
4
57
.17279
.98406
.1S995
.98179
. .20706
■97833
.22410
•97457
3
S8
.17308
.98491
.10024
.98174
.20734
.97827
.22438
•97450
2
P
•17336
.98486
.10052
.98168
.20763
.97821
.22467
•97444
I
60
•17365
.98481
.10081
.98163
.20791
.97815
•22495
^7437
0
#
Cosine
Sine
Cosine
Sine
Cosine
Sine
Cosine
Sine
/
8C
)°
7S
°
7^
;°
77
0
544
NATURAL SINES AND COSINES
13°
14°
15°
18°
f
*
Sine
Cosine
Sine
Cosine
Sine
Cosine
Sine
Cosine | '
o
.22495
•97437
.24192
.97030
.25882
.96593
.27564
.96126
60
I
.22523
•97430
.24220
•97023
.25910
•96585
•27592
.96118
59
2
.22552
.97424
.24249
•97015
•25938
.96578
.27620
.96110
S8
3
.22580
•97417
.24277
.97008
.25966
.96570
.27648
.96102
57
4
.22608
.97411
•24305
.97001
•25994
.96562
.27676
.96094
S6
5
.22637
.97404
•24333
.96994
.26022
•96555
.27704
.96086
55
6
.22665
•97398
.24362
.96987
.26050
•96547
.27731
.96078
54
7
.22693
•97391
.24390
.96980
.26079
•96540
.27759
.96070
11
8
.22722
•97384
.2441S
.96973
.26107
•96532
.27787
.96062
52
9
.22750
•97378
.24446
.96966
•26135
•96524
.27815
•96054
51
lO
.22778
•97371
.24474
•96959
.26163
•96517
.27843
.96046
50
II
.22807
•97365
.24503
.96952
.26191
.96509
.27871
.96037
49
12
.22835
•97358
.24531
•96945
.26219
.96502
.27899
.96029
48
13
.22863
•97351
•24559
•96937
.26247
•96494
.27927
.96021
47
14
.22892
•97345
•24587
.96930
•26275
.96486
.27955
.96013
46
IS
.22920
•97338
.24615
.96923
•26303
.96479
.27983
.96005
45
16
.22948
•97331
.24644
.96916
•26331
.96471
.28011
•95997
44
17
.22977
•97325
.24672
.96909
.26359
•96463
.28039
.95989
43
18
.23005
•97318
.24700
.96902
.26387
.96456
.28067
•95981
42
19
.23033
•9731 1
.24728
.96894
.26415
.96448
.28095
•95972
41
20
.23062
•97304
.24756
.96887
.26443
.96440
.28123
•95964
40
21
.23090
•97298
.24784
.96880
.26471
•96433
.28150
.95956
39
22
■23118
•97291
.24813
.96873
.26500
•96425
.28178
•95948
38
23
.23146
.97284
.24841
.96866
.26528
.96417
.28206
•95940
37
24
.23175
•97278
.24869
.96858
.26556
.96410
.28234
•95931
36
25
.23203
.97271
.24897
•96851
.26584
.96402
.28262
•95923
35
26
.23231
.97264
.24925
.96844
.26612
.96394
.28290
•9591S
34
27
.23260
.97257
•24954
•96837
.26640
.96386
.28318
•95907
33
28
.23288
.97251
.24982
.96829
.26668
•96379
.28346
•95898
3»
29
.23316
.97244
.25010
.96822
.26696
.96371
.28374
.95890
31
30
.23345
.97237
.25038
•96815
.26724
.96363
.28402
.95882
30
31
•23373
•97230
.25066
.96807
•26752
•96355
.28429
•95874
29
32
.23401
•97223
•25094
.96800
.26780
•96347
.28457
•95865
28
33
.23429
•97217
.25122
•96793
.26808
.96340
.28485
•95857
27
34
•23458
.97210
•25J51
.96786
.26836
•96332
.28513
.95849
26
35
.23486
.97203
•25179
.96778
.26864
.96324
.28541
.95841
25
36
•23514
.97196
•25207
.96771
.26892
.96316
.28569
•95832
24
37
•23542
•97189
•25235
.96764
.26920
.96308
.28597
•95824
33
38
.23571
.97182
.25263
•96756
.26948
.96301
■ .28625
•95816
22
39
.23599
.97176
•25291
•96749
.26976
.96293
.286^2
•95807
21
40
.23627
.97169
.25320
.96742
.27004
.96285
.28680 ■
•95799
20
41
.23656
.97162
.25348
■96734
•27032
.96277
.28708
•95791
19
42
.23684
•97155
•25376
•96727
.27060
.96269
.28736
•95782
18
43
•23712
.97148
.25404
•96719
.27088
.96261
.28764
•95774
17
44
.23740
.97141
•25432
.96712
.27116
•96253
.28792
.95766
16.
45
.23769
•97134
.25460
•96705
.27144
.96246
.2S820
•95757
IS
46
.23797
.97127
.25488
.96697
.27172
.96238
.28847
•95749
I'
47
.23825
.97120
.25516
.96690
.27200
•96230
.28875
•95740
li
48
.23853
•97113
.25545
.96682
.27228
.96222
.28903
•95732
ii<
49
.23882
.97106
.25573
.96675
.27256
.96214
.28931
•95724
iih
50
.23910
.97100
.25601
.96667
.27284
.96206
.28959
•95715
10
51
•23938
.97093
.25629
.96660
.27312
.96198
.28987
•95707
?
52
.23966
.97086
.25657
•96653*
.27340
.96190
.29015
.95698
8
53
•23995
•97079
.25685
.96645
.27368
.96182
.29042
•95690
54
.24023
.97072
•25713
.96638
.27396
.96174
.29070
.95681
55
•24051
•97065
.25741
.96630
.27424
.96166
.29098
•95673
56
.24079
.97058
.25769
.96623
•27452
.96158
.29126
.95664
57
.24108
•97051
•25798
.96615
.27480
•96150
.29154
•95656
58
•24136
•97044
.25826
.96608
.27508
.96142
.29182
.95647
1^
.24164
•97037
•25854
.96600
.27536
.96134
.29209
•95639
60
.241Q2
.97030
.25882
•96593
.27564
.96126
.29237
•95630
/
Cosine
Sine
Cosine
Sine
Cosine
Sine
Cosine
Sine
♦
7e
)°
7,^
>°
7^
t°
T.
J°
NATURAL SINES AND COSINES
545
170
18°
19°
20°
'
Sine
Cosine
Sine
Cosine
Sine
Cosine
Sine
Cosine
f
o
.29237
•95630
.30902
.95106
.32557
•94552
.34202
•93969
60
I
.29265
.95622
.30929
•95097
•32584
•94542
•34229
•93959
59
2
.29293
•95613
.30057
.95088
.32612
•94533
•34257
•93949
58
3
.29321
•95605
.30985
•95079
•32639
•94523
.34284
•93939
57
4
.29348
•95596
.31012
•95070
•32667
•94514
•34311
.93929
56
5
.29376
.95588
.31040
.95061
•32694
•94504
•34339
•93919
55
6
.29404
•95579
.31068
•95052
•32722
•94495
•34366
•93909
54
7
.29432
•95571
.31095
•95043
•32749
.94485
•34393
•93S99
53
8
.29460
•95562
.31123
•95033
•32777
•94476
•34421
.93889
52
9
.29487
•95554
.31151
•95024
•32804
.94466
.34448
•93879
51
10
.29515
•95545
.31178
•95015
.32832
•94457
•34475
.93869
50
11
•29543
•95536
.31206
.95006
•32859
•94447
•34503
•93859
49
12
•29571
•95528
.31233
•94997
•32887
.94438
•34530
•93849
48
J3
•29599
•95519
.31261
.94988
.32914
.94428
•34557
•93839
47
14
.29626
•95511
.31289
•94979
.32942
.94418
•34584
.93829
46
15
.29654
•95502
.31316
•94970
•32969
.94409
•34612
•93819
45
i6
.296S2
.95493
•31344
.94961
•32997
•94399
•34639
.93809
44
17
.29710
.95485
.31372
•94952
•33024
•94390
.34666
•93799
43
i8
.29737
•95476
•31399
•94943
•33051
•94380
•34694
•93789
42
19
.29765
•95467
.31427
•94933
•33079
•94370
•34721
•93779
41
20
.29793
•95459
•31454
•94924
.33106
.94361
•34748
•93769
40
21
.29821
•95450
•31482
•94915
.33134
•94351
•34775
•93759
39
22
.29849
•95441
•31510
.94906
•33161
•94342
•34803
•93748
38
23
.29876
•95433
•31537
.94897
•33189
•94332
•34830
•93738
37
24
.29904
•95424
•31565
.94888
.33216
•94322
•34857
•93728
36
25
.29932
•95415
•31593
.94878
•33244
•94313
•34884
•93718
35
26
.29960
•95407
.31620
.94869
•33271
•94303
•34912
•93708
34
27
.29987
•95398
.31648
.94860
.33298
•94293
•34939
•93698
33
28
.30015
•95389
.31675
•94851
.33326
.94284
.34966
.93688
32
29
•30043
•95380
.31703
.94842
■33353
•94274
•34993
•93677
31
30
.30071
•95372
•31730
•94832
•33381
.94264
•35021
.93667
30
31
.30098
•95363
•31758
.94823
.33408
.94254
.35048
•93657
29
32
.30126
•95354
•31786
.94814
•33436
•94245
.35075
•93647
28
33
•30154
•95345
•31813
.94805
.33463
•94235
.35102
•93637
27
34
.30182
•95337
•31841
•94795
•33490
.94225
.35130
.93626
26
35
.30209
•95328
.31868
.94786
•3351S
•94215
•35157
.93616
25
36
•30237
•95319
.31896
•94777
.33545
.94206
.35184
.93606
24
37
•30265
•95310
•31923
.94768
■33573
.94196
•35211
•93596
23
38
.30292
•95301
•3 195 1
•94758
.33600
.94186
•35239
•93585
22
39
.30320
•95293
.31979
•94749
.33627
•94176
.35266
•93575
21
40
•30348
.95284
.32006
.94740
.33655
.94167
•35293
•93565
20
41
•30376
•95275
•32034
•94730
.33682
•94157
•35-^20
•93555
'?
42
•30403
.95266
.32061
•94721
.33710
.94147
•35347
•93544
18
43
•30431
•95257
.32089
.94712
•33737
•94137
•35375
•93534
'I
44
•30459
.95248
.32116
.94702
.33764
•94127
•35402
•93524
16
45
.30486
•95240
.32144
.94693
•33792
.94118
.35429
•93514
IS
46
•30514
•95231
•32171
.94684
.33819
.94108
.35456
•93503
14
47
•30542
•95222
.32199
•94674
.33846
.94098
.35484
•93493
13
48
•30570
•95213
.32227
.94665
•33874
.94088
•35511
•93483
12
49
•30597
.95204
.32254
•94656
•33901
.94078
.35538
•93472
11
SO
•30625
•95195
.32282
.94646
•33929
.94068
.35565
.93462
10
SI
•30653
.95186
.32309
•94637
•33956
•94058
•35592
•93452
9
S2
.30680
•95177
•32337
.94627
•33983
.94049
•35619
•93441
8
S3
•30708
•95168
•32364
.94618
•34011
•94039
•35647
•93431
7
S4
•30736
•95159
•32392
.94609
.34038
.94029
•35674
•93420
6
55
•30763
•95150
•32419
•94590
•34065
.94019
•35701
•93410
S
S6
•30791
.95142
•32447
.94590
•34093
.94009
.35728
.93400
4
57
•30819
■95133
•32474
.94580
•34120
•93999
•35755
•93389
3
58
.30846
•95124
•32502
.94571
•34147
•93989
•35782
•93379
2
59
•30874
•95115
•32529
.94561
•34175
•93979
•35810
•93368
I
60
.30902
.95106
•32557
.94552
•34202
•93969
•35837
•93358
C
/
Cosine
Sine
Cosine
Sine
Cosine
Sine
Cosine
SiNI
/
7
2°
7
1°
7
0° •
6
r
546
NATURAL SINES AND COSINES
2P
Sine Cosine
•35837
.35864
•35891
•35918
•35945
•35973
.36000
.36027
•36054
.36081
.36108
•3613s
.36162
.36190
.36217
.36244
.36271
.36298
.36325
•36352
•36379
.36406
•36434
•36461
.36488
.36515
•36542
•36569
•36596
•36623
.36650
.36677
•36704
•36731
.36758
.36785
.36812
.36839
•36867
•36894
.36921
•36948
•36975
.37002
.37029
•37056
•37083
•371TO
.37137
•37164
•37191
•37218
•37245
•37272
•37299
•37326
.37353
•37380
•37407
•37434
•37461
•93358
•93348
■93337
•93327
.93316
•93306
•93295
•93285
•93274
•93264
•93253
•93243
•93232
.93222
.93211
.93201
.93190
.93180
.93169
•93159
.93148
•93137
•93127
.93116
.93106
•93095
.93084
•93074
•93063
•93052
•93042
.93031
.93020
.93010
.92999
.92988
.92978
.92967
.92956
.92945
•92935
.92924
•92913
.92902
.92892
.92881
.92870
•92859
.92849
•92838
.92827
.92816
.92805
.92794
.92784
•92773
.92762
•92751
.92740
.92729
.92718
Cosine Sine
68°
22°
Sine Cosine
.37461
.37488
•37515
•37542
.37569
.37595
.37622
.37649
•37676
•37703
•37730
•37757
•37784
.37811
•37838
.37865
•37892
•37919
.37946
.37973
•37999
.38026
.38053
.38080
.38107
.38134
.38161
.38188
.38215
.38241
.38268
•38295
•38322
•38349
•38376
.38403
•38430
•38456
•38483
•38510
•38537
•38564
•38591
•38617
•38644
•38671
.38698
•38725
•38752
•38778
•3880s
.38832
•388 1;9
.38886
.38012
•38939
.38966
•38993
.39020
.39046
•39073
.92718
•92707
.92697
.92686
•92675
.92664
•92653
.92642
.92631
.92620
.92609
.92598
•92587
•92576
.92565
.92554
•92543
•92532
.92521
.92510
.92409
.924S8
•92477
.92466
•92455
.92444
•92432
.92421
.92410
.92399
•92388
.92377
.92366
.92355
•92343
•92332
•92321
•92310
.92299
.92287
.92276
.92265
.92254
.92243
•92231
.92220
.92209
.92198
.92186
•92175
.92164
.92152
.92141
.92130
.92119
.92107
.92096
•92085
.92073
.92062
.92050
23°
Sine Cosine
Cosine Sine
67°
•39073
•39100
•39127
•39153
.39180
•39207
•39234
.39260
.39287
.39314
.39341
.39367
•39394
•39421
•39448
•39474
•39501
•39528
•39555
•39581
.39608
•39635
•39661
.39688
•39715
•39741
•39768
•39795
•39822
•39848
.39875
.39902
.39928
.39955
.39982
.40035
.40062
.40088
.40115
.40141
.40168
.40195
.40221
.40248
.40275
.40301
.40328
.40355
.40381
.40408
.40434
.40461
.40488
.40514
.40541
.40567
.40594
.4062 r
.40647
.40674
.92050
.92039
.92028
.92016
.92005
.91994
.9 1 982
.91971
.91959
.91948
.91936
.91925
.91914
.91902
.91891
•91879
.91868
•91856
.91845
•91833
.91822
.91810
.91799
.91787
.91775
.91764
.91752
.91741
.91729
.91718
.91706
.91694
.91683
.91671
.91660
.91648
.91636
.91625
.91613
.91601
.91590
.91578
.91566
.91555
.91543
.91531
.91519
.91508
.91496
.91484
.91472
.91461
.91449
.91437
.91425
.91414
.91402
.91390
.91378
.91366
.91355
24<»
Sine Cosine
Cosine Sine Cosine Sine
66° I 65=
.40674
.40700
.40727
•40753
.40780
.40806
•40833
.40860
.40886
.40913
.40939
.40966
.40992
.41019
.41045
.41072
.4109S
.41125
.41151
.41178
.41204
.41231
~*I257
,41284
.41310
•41337
41363
41390
.41416
•41443
,41469
.41496
.41522
.41549
•41575
.41602
.41628
.41655
.41681
.41707
.41734
.41760
.41787
.41813
.41840
.41S66
.41892
.41919
•41945
.41972
.41998
.42024
.42051
.42077
.42104
.42130
.42156
•42183
.42209
•42235
.42262
NATURAL SINES AND COSINES
547
25°
26° II
27° 1
28°
/
Sine (
IIOSINE
Sine
Cosine
Sine
Cosine
Sine
Cosine
'
o
.42262
90631
•43837
■89879
■45399
.89101
.46947
.88295
60
I
.42288
90618
■43863
.89867
•45425
.89087
•46973
.88281
59
2
•42315
90606
■45889
.89854
•45451
.89074
•46999
.88267
58
3
•42341
90594
.43916
.89841
•45477
.89061
.47024
.88254
57
4
.42367
90582
.43942
.89828
•45503
.89048
•47050
.88240
56
5
■42394
90569
■43968
.89816
•45529
.89035
.47076
.88226
55
6
.42420
90557
■43994
.89803
•45554
.89021
.47101
.88213
54
7
.42446
90545
.44020
.89790
•45580
.89008
.47127
.88199
53
8
•42473
90532
.44046
•89777
.45606
.88995
.47153
.88185
52
9
•42499
90520
.44072
.89764
•45632
.88981
.47178
.88172
SI
lO
•42525
90507
.44098
.89752
•45658
.88968
.47204
.88158
50
11
•42552
90495
.44124
•89739
•45684
■88955
.47229
.88144
49
12
•42578
90483
•44151
.89726
•45710
.88942
.47255
.88130
48
13
.42604
90470
•44177
•89713
•45736
.88928
.47281
.88117
47
14
•42631
90458
■44203
.89700
■45762
.88915
.47306
.88103
46
15
.42657
90446
.44229
.89687
.45787
.88902
•47332
.88089
45
i6
.42683
90433
•44255
.89674
•45813
.88888
•47358
.88075
44
17
.42709
90421
.44281
.89662
•45839
•88875
•47383
.88062
43
i8
.42736
90408
•44307
.89649
•4586s
.88862
•47409
.88048
42
19
.42762
90396
•44333
.89636
.45891
.88848
•47434
.88034
41
20
.42788
90383
•44359
.89623
.45917
•88835
.47460
.88020
40
21
•42815
90371
•44385
.89610
.45942
.88822
.47486
.88006
39
22
.42841
90358
•44411
•89597
•45968
.88808
•47511
.87993
38
23
.42867
90346
•44437
•89584
•45994
.88795
•47537
.87979
37
24
.42894
90334
.44464
.89571
.46020
.88782
•47562
.87965
36
25
.42920
90321
.44490
•8955S
.46046
.88768
•47588
.87951
35
26
.42946
90309
.44516
•89545
.46072
•8875s
•47614
•87937
34
27
.42972
90296
•44542
•89532
.46097
.88741
.47639
•87923
33
28
.42999
90284
.44568
.89519
■46123
.88728
.47665
.87909
32
29
•43025
90271
•44594
.89506
.46149
•88715
.47690
.87896
31
3°
•43051
90259
.44620
89493
•46175
.88701
.47716
.87882
30
31
•43077
90246
.44646
.89480
.46201
.88688
.47741
.87868
29
3^
.43104
90233
.44672
.89-67
.46226
.88674
•47767
•87854
28
33
•43130
9022I
.44698
■89454
.46252
.88661
•47793
.87840
27
34
•43156
90208
.44724
.89441
.46278
.88647
.47818
.87826
26
35
•43182
90196
•44750
.89428
•46304
.88634
•47844
.87812
25
36
.43209
90183
•44776
.89415
•46330
.88620
.47869
•87798
24
37
•43235
90171
.44802
.89402
•46355
.88607
•47895
.87784
23
38
■43261
90158
.44828
•89389
.46381
.88593
.47920
.87770
22
39
•43287
90146
.44854
^9376
.46407
.88580
.47946
•87756
21
40
•43313
90133
.44880
•89363
•46433
.88566
•47971
•87743
20
41
•43340
90120
.44906
•89350
•46458
•88553
•47997
•87729
19
42
•43366
90108
•44032
•89337
.46484
•88539
.48022
•87715
18
43
•43392
90095
•44958
.89324
.46510
.88526
.48048
.87701
17
44
•43418
90082
.44984
■89311
■46536
.88512
•48073
.87687
16
45
.43445
90070
.45010
.89298
■46561
.88499
.48099
•87673
IS
46
•43471
90057
•45036
.89285
■46587
.88485
.48124
•87659
14
47
■43497
90045
.45062
.89272
■46613
.88472
.48150
.87645
13
48
•43523
90032
.450SS
■89259 ■
.46639
.88458
•48175
.87631
12
49
•43549
90019
•45 1 14
.89245
.46664
.88445
.48201
.87617
11
SO
•43575
90007
•45140
.89232
.46690
.88431
.48226
■87603
10
51
.43602
89994
•45166
.89219
.46716
.88417
.48252
.87589
9
52
.43628
89981
45192
.89206
.46742
.88404
.48277
■87575
8
53
■43654
89968
•45218
■89193
.46767
.88390
•48303
■87561
7
54
.43680
89956
•45243
.89180
.46793
•88377
.48328
■87546
6
55
•43706
89943
•45269
.89167
.46819
■88363
•48354
■87532
5
56
•43733
89930
•45295
■89153
.46844
.88349
•483-9
■87518
4
57
•43759
89918
•45321
.89140
.46870
■88336
•48405
■87504
3
58
.43785
89905
•45347
.89127
.46896
.88322
.48430
.87490
2
59
.43811
89892
•45373
.89114
.46921
.88308
.48456
■87476
I
60
•43837
89879
■45399
.89101
.46947
.88295
.48481
.87462
0
t
Cosine
Sine
Cosine
Sine
Cosine
Sine
Cosine
Sine
/
64°
6;
5°
6:
2°
6]
L°
548
NATURAL SINES AND COSINES
29
0
30° 1
31
0
32° 1
/
Sine
Cosine
Sine
Cosine
Sine
Cosine
Sine
Cosine
/
o
.48481
.87462
.50000
.86603
.51504
•85717
.52992
.84805
"fc
I
.48506
.87448
.50025
.86588
•51529
•^57?^
.53017
.84789
59
2
•48532
•87434
.50050
.86573
•51554
•85687
.53041
.84774
58
3
•48557
.87420
.50076
.86559
•51579
•85672
.53066
.84759
57
4
.48583
.87406
.50101
.86544
.51604
.85657
.53091
.84743
S6
5
.48608
•87391
.50126
•86530
.51628
.85642
.53115
.84728
55
6
•48634
•87377
•50151
•86515
.51653
.85627
.53140
.84712
54
7
.48659
•87363
.50176
.86501
.51678
.85612
.53164
.84697
53
8
.48684
•87349
.50201
.86486
.51703
.85597
.53189
.84681
52
9
.48710
•87335
.50227
.86471
.51728
.85582
.53214
.84666
51
lO
•48735
•87321
.50252
.86457
•51753
.85567
.53238
.84650
50
II
.48761
•87306
.50277
.86442
•51778
.85551
.53263
.84635
49
12
.48786
.87292
.50302
.86427
.51803
.85536
.53288
.84619
48
13
.48811
.87278
•50327
•86413
.51828
.85521
.53312
.84604
47
14
•48837
.87264
•50352
.86398
.51852
.85506
■53337
.84588
46
IS
.48862
•87250
•50377
.86384
.51877
.85491
•53361
.84573
45
i6
.48888
•87235
•50403
.86369
.51902
.85476
.53386
.84557
44
17
.48913
.87221
•50428
•86354
.51927
.85461
.53411
.84542
43
i8
•48938
.87207
•50453
.86340
.51952
.85446
.53435
.84526
42
19
.48964
•87193
•50478
•86325
.51977
.85431
.53460
.84511
41
20
.48989
.87178
•50503
.86310
.52002
.85416
.53484
.84495
40
21
.49014
.87164
-50528
.86295
.52026
.85401
.53509
.84480
39
22
.49040
•87150
.50553
.86281
.52051
.85385
.53534
.84464
38
23
.49065
•87136
•50578
.86266
.52076
•85370
.53558
.84448
37
24
.49090
.87121
•50603
.86251
.52101
•85355
.53583
.84433
36
25
.49116
.87107
.50628
•86237
.52126
.85340
.53607
.84417
35
26
.49141
•87093
•50654
.86222
.52151
.85325
•53632
.84402
34
27
.49166
•87079
.50679
.86207
.52175
.85310
•53656
.84386
33
28
.49192
.87064
•50704
.86192
.52200
.85294
•53681
•84370
32
29
.49217
.87050
•50729
.86178
•52225
.85279
•53705
■84355
31
30
.49242
.87036
•50754
.86163
.52250
.85264
•53730
•84339
30
31
.49268
.87021
•50779
.86148
•52275
.85249
•53754
.84324
29
32
•49293
.87007
.50864
•86133
.52299
.85234
•53779
.84308
28
33
.49318
.86993
•50829
.86119
•52324
.85218
•53804
.84292
27
34
.49344
.86978
•50854
.86104
•52349
.85203
•53828
.84277
26
35
.49369
.86964
.50879
.86089
•52374
.85188
•53853
.84261
25
36
•49394
.86949
.50904
.86074
•52399
.85173
•53877
.84245
24
37
.49419
•86935
.50929
.86059
•52423
•85157
•53902
.84230
23
38
•49445
.86921
•50954
.86045
•52448
.85142
•53926
.84214
22
39
.49470
.86906
•50979
.86030
•52473
.85127
•53951
.84198
21
40
•49495
.86892
.51004
.86015
•52498
.85112
•53975
.84182
20
41
.49521
.86878
.51029
.86000
•52522
.85096
.54000
.84167
19
42
.49546
.86863
.51054
•85985
•52547
•^5°!l
•54024
.84151
18
43
•49571
.S6849
.51079
.85970
•52572
.85066
•54049
.84135
17
44
•49596
.86834
.51104
•85956
•52597
.85051
•54073
.84120
16
45
.49622
.86820
.51129
.85941
.52621
.85035
•54097
.84104
15
46
.49647
.86805
•51154
.85926
•52646
.85020
.54122
.84088
14
47
.49672
.86791
.51179
.85911
52671
.85005
.54146
.84072
13
48
.49697
.86777
.51204
^85896-
.52696
.84989
•54171
.84057
12
49
•49723
.86762
.51229
.85881
.52720
.84974
•54195
.84041
II
SO
.49748
.86748
•51254
.85866
•52745
.84959
.54220
.84025
10
51
•49773
•86733
.51279
•85851
•52770
.84943
.54244
.84009
9
52
•49798
.86719
•51304
•85836
•52794
.84928
.54269
.83994
8
53
.49824
.86704
•51329
.8^821
.52819
.84913
.54293
.83978
7
54
.49849
.86690
.51354
.85806
•52844
.84897
.54317
.83962
6
55
.49874
.86675
•51379
•85792
•52869
.84882
.54342
.83946
5
56
.49899
.86661
.51404
•85777
•52893
.84866
.54366
.83930
4
57
.49924
.86646
•51429
.85762
.52918
.84851
.54391
.83015
3
58
.49950
.86632
.51454
•85747
•52943
.84836
.54415
.83899
2
59
•49975
.86617
.51479
•85732
•52967
.84820
.54440
■M^^
I
60
.50000
.86603
.51504
•85717
•52992
.84805
.54464
.83867
0
T
Cosine
Sine
Cosine
Sine
Cosine
Sine
Cosine
Sine
"^
^ 6
0°
5
9°
5
3°
5
70
NATURAL SINES AND COSINES
549
33°
34°
35°
36°
t
Sine
Cosine
Sine
Cosine
Sine
Cosine
Sine
Cosine
'
o
.54464
.83867
•55919
.82904
.57358
•81915
.58779
.80902
60
I
.54488
.83851
•55943
.82887
•57381
.81899
.58802
.80885
59
2
•54513
•83835
•55968
.82871
.57405
.81882
.58826
.80867
58
3
•54537
•83819
•55992
•82855
•57429
.81865
•58849
.80850
57
4
•54561
.83804
.56016
•82839
•57453
..81848
•58873
•80833
56
5
•54586
•83788
.56040
.82822
•57477
.81832
.58896
.80816
55
6
.54610
•83772
.56064
.82806
•57501
.81815
.58920
.80799
54
7
•54635
•83756
.56088
.82790
•57524
.81798
.58943
.80782
53
8
•54659
.83740
.56112
•82773
•57548
.81782
.58967
•8076s
52
9
•54683
.83724
.56136
•82757
•57572
•81765
.58990
.80748
51
lO
.54708
•83708
.56160
.82741
•57596
.81748
.59014
.80730
50
II
•54732
83692
.56184
.82724
•57619
.81731
.59037
.80713
49
12
•54756
.83676
.56208
.82708
•57643
.81714
.59061
.80696
48
13
•54781
.83660
.56232
.82692
.57667
.81698
.59084
.80679
47
14
•54805
•83645
.56256
.82675
•57691
.81681
.59108
.80662
46
15
.54829
.83629
.56280
.82659
.57715
.81664
.59131
.80644
45
i6
•54854
•83613
•56305
■.82643
•57738
.81647
.59154
.80627
44
17
•54878
•83597
•56329
.82626
.57762
.81631
.59178
.80610
43
i8
•54902
•83581
•56353
.82610
•57786
.81614
.59201
.80593
42
19
•54927
•83565
•56377
•82593
•57810
.81597
.59225
.80576
41
20
•54951
•83549
.56401
.§2577
.57833
.81580
•59248
.80558
40
21
•54975
.83533
.56425
.82561
.57857
•81563
.59272
.80541
39
22
•54999
.83517
•56449
•82544
.57881
•81546
•59295
.80524
38
23
•55024
.83501
•56473
.82528
.57904
.81530
•59318
.80507
37
24
•55048
.83485
•56497
.82511
.57928
.81513
•59342
.80489
36
25
•55072
.83469
•56521
.82495
.57952
.81496
•59365
.80472
35
26
•55097
.83453
•56545
.82478
.57976
■81479
•59389
.80455
34
27
•55121
•83437
•56569
.82462
•57999
.81462
•59412
.80438
2,2>
28
•55145
.83421
•56593
.82446
•58023
•81445
•59436
.80420
32
29
•55169
•83405
•56617
.82429
.58047
.81428
•59459
.80403
31
30
•55194
•83389
•56641
.82413
.58070
.81412
.59482
.80386
30
31
•55218
•83373
•56665
.82396
.58094
•81395
.59506
.80368
29
32
.55242
•83356
.56689
.823 0
.58118
.81378
.59529
.80351
28
33
•55266
•83340
•56713
.82363
.58141
.81361
•59552
•80334
27
34
•55291
.83324
•56736
.82347
.58165
.81344
•59576
.80316
26
35
•55315
.83308
•56760
.82330
•58189
.81327
•59599
.80299
25
36
•55339
.83292
.56784
.82314
•58212
.81310
.59622
.80282
24
^Z
•55363
.83276
.56808
.82297
.58236
.81293
•59646
.80264
23
38
•55388
.83260
•56832
.82281
.58260
.81276
.59669
.80247
22
39
•55412
•83244
•56856
.82264
.58283
.81259
•59693
.80230
21
40
•55436
.83228
.56880
.82248
.58307
.81242
•59716
.80212
20
41
•55460
.83212
.56904
.82231
.58330
.81225
.59739
.80195
19
42
•55484
•83195
.56928
.82214
.58354
.81208
•59763
.80178
18
43
•55509
•83179
•56952
.82198
.•58378"
.81191
•59786
.80160
17
44
•55533
.83163
.56976
.82181
.58401
.81174
.59809
.80143
16
45
•55557
•83147
•57000
.82165
•58425
.81157
.59832
.80125
15
46
•55581
•83131
•57024
.82148
.58449
.81140
•59856
.80108
14
47
•55605
•83115
•57047
.82132
.58472
.81123
•59879
.80091
T'Z
48
•55630
.83098
•57071
.82115
.58496
-.81106
.59902
.80073
12
49
•55654
.83082
•57095
.82098
.58519
.81089
.59926
.80056
II
SO
•55678
.83066
•57119
.82082
.58543
.81072
•59949
.80038
10
51
•55702
.83050
•57143
.82065
•58567
.81055
•59972
.80021
9
52
•55726
•83034
•57167
.82048
•58590
.81038
•59995
.80003
8
53
•55750
.83017
•57191
.82032
•58614
.81021
.60019
.79986
7
54
•55775
.83001
•57215
.82015
•58637
.81004
.60042
.79968
6
55
•55799
.82985
•57238
.81999
.58661
.80987
.60065
•79951
5
56
.55823
.82969
.57262
.81982
.58684
.80970
.60089
•79934
4
57
•55847
•82953
.57286
.81965
•58708
•80953
.60112
.79916
3
58
•55871
.82936
.57310
.81949
•58731
.80936
.60135
•79899
2
59
•55895
.82920
.57334
.81932
•58755
.80919
.60158
.79881
I
60
•55919
.82904
•57358
•81915
•58779
.80902
.60182
.79864
0
t
Cosine
Sine
Cosine
Sine
Cosine
Sine
Cosine
Sine
T"
5f
)°
55
0
54
1
53
0
550
NATURAL SINES AND COSINES
37°
38°
39°
40°
/
Sine
Cosine
Sine
Cosine
Sine
Cosine
Sine
Cosine
'
o
.60182
.79864
.61566
.78801
.62932
•77715
•64279
.76604
60
I
.60205
.79846
.61589
•78783
•62955
.77696
•64301
.76586
59
2
.60228
.79829
.61612
.78765
.62977
•77678
•64323
•76567
58
3
.60251
.79811
.61635
•78747
.63000
.77660
■64346
•76548
57
4
.60274
•79793
.61658
■•78729
.63022
.77641
.64368
•76530
56
5
.60298
.79776
.61681
.78711
•63045
.77623
.64390
.76511
55
6
.60321
•79758
.61704
.78694
.63068
.77605
.64412
.76492
54
7
.60344
•79741
.61726
.78676
.63090
•77586
■64435
•76473
53
8
.60367
•79723
.61749
.78658
•63113
•77568
■64457
•76455
52
9 .60390
.79706
.61772
.78640
■63135
•77550
■64479
•76436
51
10
.60414
.79688
.61795
.78622
•63158
•77531
.64501
.76417
50
II
.60437
.79671
.61818
.78604
.63180
•77513
.64524
•76398
49
12
.60460
•79653
.61841
.78586
.63203
•77494
.64546
•76380
48
13
.60483
.79635
.61864
.78568
.63225
■77476
.64568
.76361
47
14
.60506
.79618
.61887
.78550
.63248
•77458
•64590
.76342
46
15
.60529
.79600
.61909
•78532
.63271
. ^77439
.64612
.76323
45
16
•60553
•79583
.61932
•78514
.63293
.77421
■64635
•76304
44
17
.60576
•79565
.61955
.78496
.63316
•77402
■64657
.76286
43
18
.60599
•79547
.61378
.78478
■63338
•77384
.64679
.76267
42
19
.60622
•79S30
.62001
.78460
■63361
•77366
.64701
.76248
41
20
.60645
.79512
.62024
.78442
•63383
•77347
■64723
.76229
40
21
.60668
•79494
.62046
.78424
.63406
•77329
.64746
.76210
39
22
.60691
•79477
.62069
.78405
.63428
•77310
.64768
.76192
38
23
.60714
•79459
.62092
•78387
■63451
.77292
.64790
•76173
37
24
.60738
.79441
.62115
.78369
■63473
•77273
.64812
•76154
36
25
.60761
.79424
.62138
•78351
■63496
•77255
.64834
•76135
35
26
.60784
.79406
.62160
.78333
.63518
.77236
.64856
.76116
34
27
.60807
•79388
.62183
.78315
•63540
.77218
.64878
.76097
33
28
.60830
•79:71
.62206
•78297
•63563
.77199
.64901
.76078
32
29
.60853
•79353
.62229
.78279
•63585
•77181
.64923
•76059
31
30
.60876
•79335
.62251
.78261
.63608
.77162
•64945
.76041
30
31
.60899
•79318
.62274
.78243
.63630
•77144
.64967
.76022
29
32
.60922
.79300
.62297
.78225
■63653
.77125
.64989
.76003
28
33
■60945
.79282
.62320
.78206
■63675
.77107
.65011
•75984
27
34
.60968
.79264
.62342
.78188
.63698
.77088
•65033
•75965
26
35
.60991
•79247
.62365
.78170
■63720
.77070
•65055
•75946
25
36
.61015
.79229
.62388
•78152
■63742
•77051
•65077
•75927
24
37
.61038
.79211
.62411
.78134
•63765
•77033
.65100
•75908
23
38
.61061
•79193
•62433
.78116
•63787
.77014
.65122
•75889
22
39
.61084
•79176
.62456
.78098
.63810
.76996
.65144
•75870
21
40
.61107
.79158
.62479
•78079
.63832
.76977
.65166
•75851
20
41
.61130
.79140
.62502
.78061
•63854
.76959
.65188
•75832
19
42
•61153
.79122
.62524
•78043
•63877
.76940
.65210
•75813
18
43
.61176
•79105
.62547
.78025
. ^63899
.76921
.65232
•75794
17
44
.61199
.79087
.62570
.78007
.63922
.76903
•65254
•75775
16
45
.61222
.79069
•62592
•77988
•63944
.76884
.65276
•75756
IS
46
.61245
•79051
.62615
•77970
.63966
.76866
.65298
•75738
14
47
.61268
•79033
.62638
•77952
■63989
.76847
.65320
•75719
13
48
.61291
•79016
.62660
•77934
.64011
.76828
•65342
.75700
12
49
.61314
.78998
.62683
•77916
■64033
.76810
.65364
.75680
II
50
•61337
.78980
.62706
•77897
.64056
.76791
•65386
.75661
10
51
.61360
.78962
.62728
•77879
.64078
.76772
.65408
•75642
9
52
.61383
.78944
.62751
.77861
.64100
.76754
•65430
•75623
8
53
.61406
.78926
.62774
•77843
.64123
.76735
•65452
•75604
7
54
.61429
.78908
.62796
.77824
.64145
•76717
•65474
•75585
6
55
.61451
.78891
.62819
.77806
.64167
.76698
.65496
•75566
5
56
.61474
.78873
.62842
•77788
.64190
.76679
.65518
.75547
4
57
.61497
.78855
.62864
•77769
.64212
.76661
•65540
•75528
3
58
.61520
•78837
.62887
•77751
•64234
.76642
.65562
•75509
2
59
•61543
.78819
.62909
•77733
•64256
.76623
•^5584
•75490
I
5o
.61566
.78801
.62932
•77715
.64279
.76604
.65606
•75471
0
/
Cosine
Sine
Cosine
Sine 1
Cosine
Sine
Cosine
Sine
/
52
0
51
1
50
°
49
0
NATURAL SINES AND COSINES
551
41°
42°
43°
44°
/
Sine
Cosine
Sine
Cosine
Sine
CoSfNE
Sine
Cosine
0
.65606
.75471
•66913
.74314
.6S200
•73135
.69466
•71934
1
.65628
.75452
•66935
.74295
.68221
.73116
.69487
.71914
2
.65650
•75433
.66956
•74276
.68242
.73096
.69508
.71894
3
.65672
•75414
.66978
.74256
.68264
.73076
.69529
•71873
4
.65694
•75395
.66999
•74327
.682S5
.7JO56
.69549
.71853
5
.65716
.75375
.67021
.74217
.68306
.73036
.69570
•71833
6
.65738
.75356
.67043
.74198
.68327
.73016
.69591
•71813
7
•65759
.75337
.67064
.74178
.68349
.72996
.69612
•71792
8
.65781
.75318
.670S6
.74159
.68370
.72976
•69633
•71772
9
.65803
•75299
.67107
•74139
.68391
.72957
.69654
•71752
10
.65825
.75280
.57129
•74120
.68412
•72937
.69675
•71732
II
.65847
.75261
.67151
.74100
.68434
•72917
.69696
.71711
12
.65869
.75241
.67172
.74080
.68455
•72897
.69717
.71691
13
.65891
.75222
.67194
.74061
.68476
•72377
•69737
.71671
14
.65913
.75203
.67215
.74041
.68497
•72857
.69758
.71650
15
.65935
.75184
.67237
.;4022
.68518
•72837
.69779
•71630
16
•65956
.75165
.67258
./4002
.68539
.72817
.69800
.71610
17
.65978
.75146
.67280
.73983
.68561
•72797
.69821
•71590
18
.66000
.75126
.67301
.73963
.68582
.72777
.69842
•71569
19
.66022
.75107
.67323
.73944
.68603
•72757
.69862
.71549
20
.66044
.75088
.67344
.73924
.68624
•72737
.69883
.71529
21
.66066
.75069
.67366
•73904
.68645
•72717
.69904
.71508
22
.66088
.75050
•673S7
.73885
.68666
.72697
.69925
.71488
23
.66109
•75030
.67409
.73865
.68688
.72677
.69946
.71468
24
.66131
.75011
.67430
•73846
.68709
•72657
.69966
•71447
25
.66153
.74992
.67452
.73826
.68730
.72637
.69987
.71427
26
.66175
•74973
.67473
.73806
.68751
.72617
.70008
.71407
27
.66197
•74953
.67495
•73787
.68772
•72597
.70029
•71386
28
.66218
•74934
.67516
•73767
.68793
•72577
.70049
.71366
29
.66240
•7491 5
.67538
•73747
.68814
.72557
.70070
.71345
30
.66262
.74896
.67559
•73728
.68835
•72537
.70091
•71325
31
.66284
.74876
.67580
.73708
.68857
.72517
.70112
.71305
32
.66306
•74857
.67602
.73688
.68878
.72497
.70132
.71284
33
.66327
.74838
.67623
•73669
.68899
.72477
.70153
.71264
34
.66349
.74818
.67645
•73649
.68920
•72457
.70174
.71243
35
.66371
•74799
.67666
,73629
.68941
•72437
.70195
.71223
36
•66393
•74780
.67688
•73610
.68962
.72417
.70215
.71203
37
.66414
.74760
.67709
.73590
.68983
•72397
.70236
.71182
38
.66436
•74741
.67730
.73570
.69004
.72377
.70257
.71162
39
.66458
•74722
.67752
.73551
.69025
.72357
.70277
.71141
40
.66480
•74703
.67773
•73531
.69046
•72337
.70298
.71121
41
.66501
•74683
.67795
.73511
.69067
•72317
.70319
.71100
42
.66523
.74664
.67816
.73491
.69088
.72297
.70339
.71080
43
.66545
.74644
.67837
.73472
.69109
.72277
.70360
.71059
44
.66566
.74625
.67859
.73452
.69130
.72257
.70381
.71039
45
.66588
.74606
.67^80
.73432
.69151
.72236
.70401
.71019
46
.66610
.74586
.67yoi
.73413
.69172
.72216
.70422
.70998
47
.66632
•74567
.67923
•73393
.69193
.72196
.70443
.70978
48
.66653
•74548
.67944
•73373
.69214
.72176
.70463
.70957
49
.66675
.74528
.67965
•73353
■69235
.72156
.70484
■70937
50
.66697
•74509
.67987
•73333
.69256
•72136
.70505
.70916
51
.66718
.74489
.68008
•73314
.69277
.72116
.70525
.70896
52
.66740
.74470
.68029
•73294
.69298
.72095
.70546
.70875
53
.66762
•74451
.68051
•73274
.69319
.72075
.70567
.70855
54
.66783
•74431
.68072
•73254
•69340
•72055
.70587
.70834
55
.66805
•74412
.68093
.73234
.69361
•72035
.70608
.70813
56
.66827
•74392
.68115
.73215
.69382
.72015
.70628
.70793
57
.66848
•74373
.68136
.73195
.69403
.71995
.70649
.70772
58
.66870
•74353
.68157
.73175
.69424
.71974
.70670
.70752
59
.66891
•74334
.68179
.73155
.69445
•71954
.70690
.70731
60
.66913
•74314
.68200
.73135
.69466
.71934
.70711
.70711
Cosine
Sine
Cosine
Sine
Cosine
Sine 1
1
Cosine
Sine
4S
°
47
0
46
45
0
552
NATURAL SECANTS AND CO-SECANTS
0
°
L°
2°
3°
*
Sec.
Co-sec.
-Sec.
Co-sec.
Sec.
Co-sec.
Sec.
Co-sec.
'
o
I
Infinite.
I.Ov-OI
57-299
1.0006
28.654
1.0014
19.107
60
I
I
3437-70
I.OOOI
56-359
1 .0006
28.417
1.0014
19.002
59
2
I
1718.90
1.0002
55 -450
1 .0006
28.184
1.0014
18.897
58
3
I
1145.90
1 .0002
54-570
1 .0006
27-955
1.0014
18.794
57
4
I
859-44
1.0002
53-/I8
1.0006
27-730
1.0014
18.692
56
5
I
687.55
1 .0002
52-891
1.0007
27-508
1.0014
18.591
55
6
I
572.96
1.0002
52.090
1.0007
27.290
1.0015
18.491
54
7
I
491. II
1 .0002
51-313
1.0007
27-075
1.0015
18.393
53
8
I
429.72
1 .0002
50-558
1.0007
26.864
1.0015
18.295
52
9
I
381-97
1 .0002
49826
1.0007
26.655
1.0015
18.198
51
lO
I
343-77
1.0002
49-114
1.0007
26.450
1. 001 5
18.103
50
II
I
■312-52
1.0002
48.422
1.0007
26.249
1.0015
18.008
49
12
I
286.48
1.0002
47-750
1.0007
26.050
1.0016
17-914
48
13
I
264.44
1.0002
47.096
1.0007
25-854
1.0016
17.821
47
14
I
245.55
1.0002
46.460
1.0008
25.661
1.0016
17-730
46
^S
I
22>l8
1.0002
45.840
1.0008
25-471
1.0016
17-639
45
i6
I
214.86
1.0002
45-237
1.0008
25-284
1.0016
17-549
44
17
I
202.22
1.0002
44.650
1.0008
25.100
1 .00 1 6
17-460
43
i8
I
190.99
1.0002
44.077
1.0008
24-918
1.0017
17-372
42
19
I
180.73
1 .0003
43-520
1.0008
24-739
1.0017
17-285
41
20
I
171-89
1.0003
42.376
1.0008
24.562
1. 001 7
17-198
40
21
I
163.70
1.0003
42-445
1.0008
24-358
1.0017
17.113
39
22
I
156.26
1 .0003
41.928
1.0008
24.216
1.0017
17.028
38
23
I
149.47
1.0003
41-423
I 0009
24.047
1.0017
16.944
37
24
I
143-24
1.0003
40.930
1.0009
23.880
1.0018
16.861
36
25
I
137-51
1 .0003
40.448
1.0009
23-716
1.0018
16.779
35
26
I
132.22
1 .0003
39-978
1 .0009
23-553
1.0018
16.698
34
27
I
127.32
1.0003
39-518
1.0009
23-393
1.0018
16.617
33
28
I
122.78
1 .0003
39.069
1.0009
23-235
1.0018
16.538
32
29
I
H8.54
1.0003
38.631
1 .0009
23.079
1.0018
16.459
31
30
I
114-59
1.0003
38.201
1.0009
22.925
1.0019
16.380
30
31
I
110.90
1 .0003
37-782
I.OOIO
22.774
1.0019
16.303
29
32
I
107-43
1 .0003
37-371
1. 0010
22.624
1.0019
16.226
28
33
I
104.17
1 .0004
36.969
I.OOIO
22.476
1-0019
16.150
27
34
I
lOI.II
1.0004
36.576
1.0010
22.330
1.0019
16.075
26
3|
I
95=223
1 .0004
36.191
1.0010
22.186
1.0019
16.000
25
36
I
9540*5
1.0004
35-814
I.OOIO
22.044
1.0020
15.926
24
37
I
92.914
1 .0004
35-445
I.OOIO
21.904
1.0020
15-853
23
38
1. 000 1
92.469
1 .0004
35-084
1.0010
21.765
1 .0020
iS-780
22
39
1. 000 1
88.149
1 .0004
34-729
I.OOII
21.629
1.0020
15-708
21
40
1. 000 1
85.046
1 .0004
34-382
1. 001 1
21.494
1 .0020
15.637
20
.41
1. 000 1
83.849
1 .0004
34.042
I.OOII
21.360
1.0021
15.566
19
42
1. 000 1
81.853
1 .0004
33-708
I.OOII
21.228
1.0021
15-496
18
43
I.OOOI
79-950
1.0004
33-381
I.OOII
21.098
T.0021
15-427
17
44
1. 0001
78.133
1 .0004
33-060
I.OOII
20.970
1. 002 1
15-358
16
"*!
I.OOOI
76.396
1.0005
32.745
I.OOII
20.843
1.0021
15-290
15
46
I.OOOI
74-736
1.0005
32.437
1. 0012
20.717
1.0022
15.222
ij
47
I.OOOI
73-146
1.0005
.32-134
I.OOI2
20.593
1.0022
15-155
13
48
I.OOOI
71.622
1 .0005
31.836
1.0012
20.471 •
1.0022
15-089
12
49
I.OOOI
71.160
1.0005
31-544
1.0012
20.350
1.0022
15-023
II
SO
I.OOOI
68.757
1.0005
31.257
1.0012
20.230
1.6022
14-958
10
SI
I.OOOI
67.409
1.0005
30-976
1.0012
20.112
1.0023
14-893
9
52
I.OOOI
66.m
1 .0005
30.699
1. 001 2
19-995
1.0023
14.829
8
53
I.OOOI
64.S66
1 .0005
30-428
I.00I3
19.880
1.0023
14-765
7
54
I.OOOI
63.664
1 .0005
30.161
1.0013
19.766
1.0023
14.702
6
55
I.OOOI
62 507
1 .0005
29.899
1.0013
I9.'^'53
1.0023
14.640
5
56
I.OOOI
61.391
1 .0006
29.641
1.0013
19-541
1.0024
14-578
4
57
I.OOOI
61.314
1.0006
29-388
1.0013
19-431
1.0024
14-517
3
58
I.OOOI
59-274
1.0006
29.139
1.0013
19.322
1.0024
14.456
2
59
I.OOOI
58.270
1.0006
28.S94
1.0013
19.214
1.0024
14-395
I
60
I.OOOI
57-299
1 .0006
28.654
1.0014
19.107
1.0024
14-335
0
Co-sec.
Sec.
Co-sec
Sec.
Co-sec.
Sec.
Co-sec.
Sec.
8i
r
8^
1°
8
r
8(
5°
NATURAL SECANTS AND CO-SECANTS
553
40
5°
f
Sec.
Co-SEC.
Sec.
Co-sec.
o
1.0024
14-335
1.0038
11.474
1
1.0025
14.276
0038
11.436
2
1.0025
14.217
0039
11.398
3
1.0025
14-159
0039
1 1 .360
4
1. 002 5
14.101
0039
11-323
5
1.0025
14.043
0039
11.286
6
1.0026
13-986
0040
11.249
7
1.0026
13-930
0040
11.213
8
1.0026
13-874
0040
11. 176
9
1 .0026
13.818
0040
11.140
lO
1.0026
13-763
0041
11.104
11
1.0027
13-708
0041
11.069
12
1.0027
13-654
0041
11.033
T-J,
1.0027
13.600
0041
10.988
14
1.0027
13-547
0042
10.963
IS
1.0027
13-494
0042
10.929
i6
1.0028
13-441
0042
10.894
17
1.0028
13-389
0043
10.860
i8
1.0028
13-337
0043
10.826
19
1.0028
13.2S6
0043
10.792
20
1.0029
13-235
0043
10.758
21
1.0029
13-184
0044
10.725
22
1.0029
13.134
0044
10.692
23
1.0029
13.084
0044
10.659
-24
1.0029
13-034
0044
10.626
25
1 .0030
12.985
0045
10.593
26
1.0030
12.937
0045
10.561
27
1.0030-
12.888
0045
10.529
28
1 .0030
12.840
0046
10.497
29
1.0031
12.793
0046
10.465
30
1.0031
12.745
0046
10.433
31
1.0031
12.698
0046
10.402
32
1.0031
12.652
0047
10.371
33
1.0032
12.606
0047
10.340
34
1.0032
12.560
0047
10.309
35
1 .0032
12.514
0048
10.278
3^
1.0032
12.469
0048
10.248
37
1.0032
12.424
0048
10.217
38
1 .0033
12.379
0048
10.187
39
1.0033
12-335
0049
10.157
40
I -0033
12.291
0049
10.127
41
I -0033
12.248
0049
10.098
42
1.0034
12.204
0050
10.068
43
1.0034
12.161
0050
10.039
44
1.0034
12. 118
0050
10.010
45
1.0034
12.076
0050
9.9812
46
1-0035
12.034
0051
99525
47
I -0035
11.992
0051
9.9239
48
1-0035
11.950
0051
9.8955
49
1-0035
11.909
0052
9.8672
SO
1 .0036
11.868
0052
9-8391
51
1.0036
11.828
0052
9.81T2
52
1 .0036
11.787
0053
9-7834
53
1 .0036
11.747
0053
9.7558
54
1.0037
11.707
0053
9-7283
55
1.0037
11.668
0053
9.7010
56
1.0037
11.628
0054
9.6739
57
1.0037
11.589
0054
9.6469
58
1.0038
11.550
0054
9.6200
59
1.0038
11.512
0055
9-5933
60
1 .0038
11.474
I -005 s
9.5668
t
Co-SEC.
Sec
Co-six:.
Sec.
8.
5°
8
40
6
0
1 7°
Sec.
Co-SEC
Sec
Co-SEC
r
I.005S
9.5668
1.0075
8.2055
60
1.0055
9.5404
1.007s
8.1861
59
1.0056
9-5I4I
1.0076
8.1668
58
1 .0056
9.4880
1.0076
8.1476
57
1.G056
9.4620
1.0076
8.1285
56
1.0057
9.4362
1.0077
8.1094
55
1.0057
9.4105
1.0077
8.0905
54
r.oos7
9-3850
1.0078
8.0717
53
1.0057
9-3596
1.0078
8.0529
52
1.0058
9-3343
1.0078
8.0342
51
1.0058
9.3092
1.0079
8.0156
50
1.0058
9.2842
1.0079
7.9971
49
1.0059
9-2593
1.0079
7-9787
48
1.0059
9-2346
1.0080
7-9604
47
1.0059
9.2100
1.0080
7-9421
46
! 1.0060
9.1855
i.ooSo
7.0240
45
1.0060
9.1612
1.0081
7-0059
44
1 .0060
9-1370
1.0081
7-8879
43
1 1.0061
9.1129
1.0082
7.8700
42
1.0061
9.0890
1.0082
7-8522
41
1. 006 1
9.0651
1.0082
7.8344
40
1 .0062
9.0414
1.0083
7.8168
39
I 0062
9.0179
1.0083
7.7992
38
1.0062
8.9944
1 .0084
7-7817
37
1 .0063
8.9711
1.0084
7.7642
36
1.0063
8.9479
1.0084
7.7469
35
1.0063
8.9248
1 .0085
7.7296
34
1 .0064
8.9018
1.0085
7.7124
33
1 .0064
8.8790
1 .0085
7.6953
32
1 .0064
8.8=;63
1.0086
7-6783
31
1 .0065
8.8337
1.0086
7.6613
30
1.0065
8.8112
1.0087
7.6444
29
1 .0065
8.7888
1.0087
7.6276
28
1 .0066
8.766s
1.0087
7.6108
27
1.0066
8.7444
1.0088
7.5942
26
1 .0066
8.7223
1.0088
7.5776
25
1 .0067
8.7004
1 .0089
7.5611
24
1.0067
8.6786
1.0089
7.5446
23
1.0067
8.C569
1.0089
7.528£
22
1.0068
8-6353
1.0090
7.5119
21
1.0068
8.6138
i'oo90
7.4957
20
1.0068
8.5924
1.0090
7-4795
19
10069
8.5711
1. 009 1
7.4634
18
1 .0069
8.5499
1. 0091
7.4474
17
1.0069
8.5289
1.0092
7.4315
16
1.0070
8.5079
1.0092
7.4156
15
1.0070
8.4871
1 .0092
7.3998
14
1.0070
8.4663
1.0093
7.3840
13
1.0071
8.4457
1.0093
7.3683
12
1. 0071
8.4251
1 .0094
7-3527
11
1.0071
8.4046
1.0094
7-3372
10
1.0072
8.3843
1.0094
7-3217
9
1.0072
8.3640
1 .0095
7-3063
8
1.0073
8.3439
1.0095
7.2909
7
1-0073
8.3238
1 .0096
7-2757
6
1.0073
8.3039
1 .0096
7.2604
5
1.0074
8.2840
1 .0097
7.2453
4
1.0074
8.2642
1 .0097
7.2302
3
1.0074
8.2446
1 .0097
7.2152
2
1.0075
8.2250
1 .0098
7.2002
I
1.0075
8.2055
1.0098
7-1853
0
Co-SEC
Sec
Co-SEC.
Sec
T
y s:
J°
&
2°
554
NATURAL SECANTS AND CO-SECANTS
8°
9°
10°
11°
/
Sec.
Co-SEC.
Sec.
Co-SEC.
Sec.
CO.SEC.
Sec.
Co-SEC.
'
o
1.0098
7-1853
1.0125
6.3924
1.0IS4
5-7588
1.0187
5.2408
60
I
1.0099
7.1704
1.0125
6.3807
1-OIS5
5-7493
i.oiSS
5-«330
59
2
1.0099
7-1557
1.0125
6.3690
1-0155
5-7398
1.0188
5.2252
58
3
1.0099
7.1409
1.0126
6.3574
1.0156
5-7304
1.0189
5.2174
57
4
1. 0100
7.1263
1.0126
6-3458
1.0156
5-7210
1.0189
5.3097
56
I
1. 0100
7.1117
1.0127
6-3343
1.0157
5-7117
1.0190
5.2019
55
6
I.OIOI
7.0972
1.0127
6.3228
1.0157
5-7023
1.0191
5.1942
54
7
I.OIOI
7-0827
1.0128
6.3113
1.0158
5-6930
1.0191
5.1865
53
S
1. 0102
7-0683
1.0128
6.2999
1.0158
5-6838
1.0192
5.1788
52
9
I.0I02
7-0539
1.0129
6.288s
1-0159
5-6745
1.0192
5.1712
SI
lO
I.0I02
7.0396
1.0129
6.2772
1.0159
5.6653
1-0193
5.1636
50
II
I.OIO3
7.0254
1.0130
6.2659
1.0160
5-6561
1.0193
5.1560
49
12
1.0103
7.0112
1.0130
6.2546
1. 0160
5-6470
1.0194
5.1484
48
13
1. 0104
6.9971
1.0131
6-2434
1.0161
5-6379
1-0195
5.1409
47
14
1.0104
6.9830
1-0131
6.2322
1.0162
5.62S8
1.0195
5.1333
46
15
1. 0104
6.9690
1.0132
6.2211
1^162
5-6197
1.0196
5.1258
45
i6
I.OIO5
6.9550
1.0132
6.2100
1.0 163
5-6107
1.0196
5.1183
44
17
I.OIO5
6.9411
1-0133
6.1990
1.0163
5-6017
1. 01 07
5.1109
43
i8
I.OI06
6.9273
1-0133
6.1880
1.0164
5-5928
1.0198
5.1034
42
19
I.OI06
6.9135
1.0134
6.1770
1.0164
5-5838
1.01 e8
5-0960
41
20
I.OIO7
6.8998
1.0134
6.1661
1.0165
5-5749
1.0199
5.0886
40
21
I.OIO7
6.8861
1-0135
6.1552
1.0165
5-5660
1.0199
5.0812
39
22
I.OI07
6.8725
1-OI35
6.1443
1.0166
5-5572
1.0200
5.0739
38
23
1. 0108
6.8<;89
1.0136
6.1335
1.0166
5-5484
1.0201
5.0666
37
24
I.OI08
6-8454
1.0136
6.1227
1.0167
5 -50^6
1.0201
S.0593
36
25
1.0109
6.8320
1.0136
6.1120
1.0167
5-5308
1.0202
5.0520
35
26
1. 0109
6.8185
1.0137
6.1013
1.0168
5-5221
1.0202
5-0447
34
27
I.OIIO
6.8052
1-0137
6.0906
1.0169
5-5134
1.0203
50375
Z3
28
l.OIIO
6.7919
1.0138
6.0800
1.0169
5-5047
1.0204
5.0302
32
29
I.OIII
6.7787
1.0138
6.0694
1. 01 70
5-4960
1.0204
5.0230
31
30
I.OIII
6.7655
1.0139
6.0588
1.0170
5.4874
1.0205
5-0158
30
31
i.om
6.7523
1.0139
6.0483
1.0171
5-4788
1.0205
5-0087
29
32
1.0112
6.7392
1.0140
6.0379
1.0171
5-4702
1.0206
5-0015
28
33
1.0112
6.7262
1.0140
6.0274
1.0172
5-4617
1.0207
4.9944
27
34
1.0113
6.7132
1.0141
6.0170
1. 01 72
5-4532
1.0207
• 4-9873
26
35
1.0113
6.7003
1.0141
6.0066
1.0173
5-4447
1.0208
4.9802
25
36
1.0114
6.6874
1.0142
59963
1.0174
5-4362
1.0208
4-9732
24
H
1.0114
6.6745
1.0142
5.9860
1.0174
5-4278
1.0209
4.9661
23
38
1^115
6.6617
1.0143
5-9758
1-0175
5-4194
1.0210
4-9591
22
39
1.0115
6.6490
1-0143
5-9655
1-0175
S.4110
1.0210
4-9521
21
40
1.0115
6.6363
1.0144
5-9554
1.0176
5-4026
1.0211
4-9452
20
41
1.0116
6.6237
1.0144
5-9452
1.0176
5-3943
1.0211
4-9382
19
42
1.0116
6.6111
1.0145
5-9351
1.0177
5-3860
1.0212
4-9313
18
43
1.0117
6.5985
1-0145
5-9250
1.0177
5-3777
1.0213
4.9243
17
44
1.0117
6.5860
1.0146
5-9150
1.0178
5-3695
1.0213
4-9175
16
45
1.0118
6.5736
1.0146
5.9049
1.0179
5-3612
1.0214
4.9106
IS
46
1.0118
6.5612
1.0147
5-8950
1.0179
5-3530
1.0215
4-9037
14
47
1.0119
6.5488
1.0147
S-8850
1.0180
5 3449
1.0215
4.8969
13
48
1.0119
6.5365
1.0148
5-8751
1.0180
5-3367
1.0216
4-8901
12
49
1.0119
6.5243
1.0148
5-8652
1.0181
5-3286
1.0216
4-8833
II
SO
1. 01 20
6.5121
1.0149
5-8554
1.0181
5-3205
1.0217
4.8765
10
51
1. 01 20
6.4999
1.0150
5.8456
1.0182
5-3124
1.0218
4-8697
9
52
1.0121
6.4878
1.0150
5-8358
1.0182
5-3044
1.0218
4.8630
8
S3
1.0121
6.4757
1.0151
5.8261
1.0183
5-2963
1.0219
4-8563
7
S4
1.0122
6-4637
1.0151
5-8163
1.0184
5-2883
1.0220
4.8496
6
55
1. 01 22
6-4517
1.0152
5-8067
1.0184
5-2803
1.0220
4.8429
S
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1.0123
6.4398
1.0152
5-7970
1.0185
5-2724
1.0221
4.8362
4
57
1.0123
6.4279
1-0153
5-7874
1.0185
5-2645
1.0221
4.8296
3
58
1. 01 24
6.4160
1-0153
5-7778
1.0186
5-2566
1.0222
4.8229
2
59
1.0124
6.4042
1.0154
5-7683
1.0186
5-2487
1.0223
4.8163
I
60
1.0125
6-3924
1.0154
5-7588
1.0187
5-2408
1.0223
4.8097
0
~r
Co-SEC.
Sec.
Co-SEC.
Sec.
Co-SEC.
Sec
Co-SEC.
Sec.
81
0
8(
r
7S
1°
7S
°
NATURAL SECANTS AND CO-SECANTS
555
12°
13° !
140
15°
/
Sec.
Co-sec.
Sec.
Co-sec.
Sec.
Co-SEC.
Sec.
Co-SEC.
'
o
1.0223
4.8097
1.0263
4-4454
1.0306
4.1336
1.0353
3-8637
60
I
1.0224
4.8032
1.0264
4.4398
1.0307
4.1287
I.0353
3.8595
59
2
I.022S
4.7966
1.0264
4.4342
1.0308
4.1239
1.0354
3.8553
58
3
1.0225
4.7901
1.0265
4-4287
1 .0308
4.II9I
I.035S
3-8512
57
4
1.0226
4-7835
1.0266
4-4231
1.0309
4.II44
1.0356
3.8470
56
5
1.0226
4-7770
1.0266
4.4176
1.0310
4.1096
I.03S7
3.8428
55
6
1.0227
4-7706
1.0267
4.4121
1.0311
4.1048
1.0358
3.8387
54
7
1.0228
4.7641
1.0268
4.4065
1.0311
4.IOOI
1.0358
3-8346
53
8
1.0228
4-7576
1.0268
4.401 1
1.0312
4.0953
1.0359
3.8304
52
9
1.0229
4-7512
1.0269
4-39S6
1.0313
4.0906
1.0360
3-8263
51
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1.0230
4.7448
1.0270
4.3910
1.0314
4.0859
1.0361
3.8222
50
11
1.0230
4.7384
1.0271
4-3847
1.0314
4.0812
1.0362
3.8181
49
12
1.0231
4-7320
1.0271
4-3792
1.0315
4.0765
1.0362
3.8140
48
13
1.0232
4-7257
1.0272
4-3738
1.0316
4.0718
1.0363
3.8100
47
14
1.0232
4-7193
1.0273
4.3684
1.0317
4.0672
1.0364
3.8059
46
15
1.0233
4-7130
1.0273
4-3630
1.0317
4.0625
1.0365
3.8018
45
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1.0234
4.7067
1.0274
4-3576
1.0318
4.0579
1.0366
3.7978
44
17
1.0234
4.7004
1.0275
4.3522
1.0319
4.0532
1.0367
3.7937
43
1 8
I-023S
4.6942
1.0276
4-3469
1.0320
4.0486
1.0367
3.7897
42
19
I-0235
4.6879
1.0276
4-3415
1.0320
4.0440
1.0368
3.7857
41
20
1.0236
4.6817
1.0277
4-3362
1.0321
4.0394
1.0369
3.7816
40
21
1.0237
4-6754
1.0278
4-3309
1.0322
4.0348
10370
3.7776
39
22
1.0237
4.6692
1.0278
4-3256
1.0323
4.0302
1.0371
3.7736
38
23
1.0238
4-6631
1.0279
4-3203
1.0323
4.0256
1.0371
3.7697
37
24
1.0239
4.6569
1.0280
4-3150
1.0324
4.02 1 1
1.0372
3.7657
36
25
1.0239
4-6507
1.0280
4.3098
1.0325
4.0165
1.0373
3.7617
35
26
1.0240
4.6446
1.0281
4.3045
1.0326
4.0120
1.0374
3.7577
34
27
1.0241
4-6385
1.0282
4.2993
1.0327
4.0074
1.0375
3.7538
33
28
1.0241
4.6324
1.0283
4.2941
1.0327
4.0029
1.0376
3.7498
32
29
1.0242
4.6263
1.0283
4.2888
1.0328
3.9984
1.0376
3.7459
31
30
1.0243
4.6202
1.0284
4.2836
1.0329
3-9939
1.0377
3.7420
30
31
1.0243
4.6142
1.0285
4-2785
1-0330
3.9894
1.0378
3.7380
29
32
1.0244
4.6081
1.0285
4.2733
1-0330
3-9850
1.0379
3.7341
28
33
1.0245
4.6021
1.0286
4-2681
1.0331
3-9805
1.0380
3.7302
27
34
1.0245
4-5961
1.0287
4.2630
1.0332
3-9760.
1. 0581
3.7263
26
35
1.0246
4-5901
1.0288
4.2579
1-0333
3.9716
1.0382
3.7224
25
36
1.0247
4-5841
1.0288
4.2527
1.0334
3.9672
1.0382
3.7186
24
37
1.0247
4-5782
1.0289
4.2476
1-0334
3-9627
1.0383
3-7147
23
38
1.0248
4-5722
1.0290
4.2425
1-0335
3-9583
1.0384
3.7108
22
39
1.0249
4-5663
1. 0291
4.2375
1.0336
3-9539
1.0385
3.7070
21
40
1.0249
4-5604
1. 0291
4.2324
I-0337
3-9495
1.0386
3.7031
20
41
1.0250
4-5545
1.0202
4.2273
1-0338
3.9451
1.0387
3.6993
19
42
1-0251
4-5486
1.0293
4.2223
1.033S
3.9408
1.0387
36955
18
43
1.0251
4-5428
1.0293
4.2173
1.0339
3.9364
1.0388
3.6917
17
44
1.0252
4-5369
1.0294
4.2122
1.0340
3.9320
1.0389
3.6878
16
45
I-0253
4-53II
1.0295
4.2072
1.0341
3.9277
1.0390
3.6840
IS
46
1.0253
45253
1.0296
4.2022
1.0341
3.9234
1.0391
3.6802
14
47
1.0254
4-519S
1.0296
4.1972
1.0342
3.9199
1.0392
3.6765
13
48
I.0255
4-5137
1.0297
4.1923
1.0343
3.9147
1 .0393
3.6727
12
49
1.02S5
4-5079
1.0298
4.1873
1.0344
3.9104
1.0393
3.6689
II
50
1.0256
4-502I
1.0299
4.1824
1.0345
3.9061
1.0394
3.6651
10
SI
1.0257
4.4964
1.0299
4.1774
1.0345
3.9018
1-0395
3.6614
0
52
1.0257
4.4907
1 .0300
4.1725
1.0346
3.8976
1.0396
3.6576
8
53
1.0258
4.4850
1. 030 1
4.1676
1.0347
3.8933
1 .0307
3-6539
7
54
1.0259
4-4793
1.0302
4.1627
1.0348
3.8990
1-0308
3.6502
6
55
1.0260
4-4736
1.0302
4.1578
1.0349
3.8848
1.0309
3.6464
5
56
1.0260
4-4679
1.0303
4.i'^29
1.0349
3.8805
1.0399
3.6427
4
H
1.0261
4-4623
1-0304
4.1481
1.0350
3.8763
1 .0400
3.6390
3
58
1.0262
4.4566
1-0305
4.1432
1.0351
3.8721
1. 040 1
36353
2
59
1.0262
4.4510
1-0305
4.1384
1.0352
3.8679
1.0402
3.6316
1
60
1.0263
4-4454
1.0306
4.1336
1.0353
3.8637
1 .0403
3.6279
0
T"
Co-sec.
Sec.
Co-sec.
Sec.
1 Co-SEC.
Sec
Co-SEC.
Sec
~r
T
r°
7(
3°
1 7.
5°
7
i°
556
NATURAL SECANTS AND CO-SECANTS
16*^
170
18°
19°
Sec.
Co-sec.
Sec.
Co-sec.
Sec.
Co-sec.
Sec.
Co-SEC.
»
1.0403
3.6279
1-0457
3-4203
1-0515
3.2361
1.0576
3.0715
60
1.0404
3-6243
1-0458
3-4170
1.0516
3-2332
1-0577
3.0690
59
1.0405
3.6206
I.C459
3-4138
1.0517
3-2303
1.0578
3-0664
58
1.0406
3-6169
1.0460
3.4106
1.0518
3.2274
I-OS79
30638
57
1 .0406
3-6x33
1. 046 1
3-4073
I -05 19
3-2245
1-0580
3-0612
56
1.0407
3.6096
1.0461
3-4041
1.0520
3.2216
1.0581
3-0586
55
1 .0408
3.6060
1.0462
3.4009
1.0521
3.2188
1.0582
3.0561
54
1.0409
3-6024
1.0463
3-3977
1.0522
3-2159
1.0584
3-0535
S3
1. 0410
3.5987
1.0464
3-3945
1-0523
3.2131
1.0585
3-0509
52
1.0411
3-5951
1.0465
3-3913
1.0524
3.2102
1.0586
3-0484
51
1.0412
3.5915
1 .0466
S-3881
1-0525
3.2074
1.0587
3-0458
50
1. 0413
3.5879
1.0467
3-3849
1.0526
3.2045
1.0588
3-0433
49
1. 0413
3.5S43
1.0468
3-3817
1.0527
3-2017
1.0589
3-0407
48
1.0414
3-5807
1.0469
3-3785
1.0528
3.1989
1.0590
3-0382
47
1-0415
3-5772
1.0470
3-3754
1.0529
3-1960
1.0591
3-0357
46
1.0416
3-5736
1.0471
3-3722
1.0530
3-1932
1.0592
3-0331
45
1.0417
3-5700
1.0472
3.3690
1.0531
3-1904
1-0593
3-0306
44
1.0418
3-5665
1-0473
3-3659
1.0532
^•'f76
1.0594
3.0281
43
1.0419
3.5629
1.0474
3-3627
I -0533
3.1848
1-0595
3.0256
42
1.0420
3-5594
1-0475
3-3596
1-0534
3.1820
1-0596
3-0231
4t
1.0420
3-5559
1.0476
3-3565
I-053S
3.1792
1-0598
3-0206
40
1. 042 1
3-5523
1.0477
3-35,34
1.0536
3-1764
1-0599
3.0181
39
1.0422
3-5488
1.0478
3-3502
1.0537
3-1736
1 -0600
30156
38
1.0423
3-5453
1.047S
3-3471
1.0538 •
3-1708
i.o6oi
3-0131
37
1.0424
3-5418
1.0479
3-3440
I.0539
3.1681
1.0602
3-0106
36
1.0425
3.5383
1 .0480
3-3409
1.0540
3-1653
1.0603
3.0081
35
1.0426
3-5348
1.0481
3-3378
1.0541
3.1625
1 .0604
3-0056
34
1.0427
3-5313
1.0482
3-3347
1.0542
3.1598
1.0605
3-0031
33
1.0428
3.5279
1-0483
3-3316
I -0543
3.1570
1. 0606
3-0007
32
1.0428
3.5244
1-0484
3-3286
1-0544
3-1543
1.0607
2.9982
31
1.0429
3.5209
1.0485
3-3255
1-0545
3-1515
1.0608
2-9957
30
1.0430
3-5175
1.0486
3-3224
1.0546
3.1488
1.0609
2-9933
29
1.0431
3.5140
1.0487
3-3194
1-0547
3-1461
1.06 1 1
2.9908
28
1.0432
3.5106
1.0488
3-3163
1.0548
3-1433
1.0612
2.9884
27
1 .0433
3-5072
.1.0489
3-3133
1.0549
3.1406
1-0613
2.9859
26
1.0434
3.5037
1.0490
3-3102
I -0550
3.1379
1.0614
2.9835
25
1.043 s
3-5003
1.0491
3-3072
1-0551
3-1352
1.0615
2.9810
24
1.0436
3.4969
1.0492
3-3042
1-0552
3-1325
1.0616
2.9786
23
I -0437
3-4935
1-0493
3-30II
1-0553
3-1298
1. 061 7
2.9762
22
1.0438
3.4901
1.0494
3-2981
I -0554
3-1271
1.0618
2.9738
21
1.0438
3-4867
1.0495
3-2951
1-0555
3-1244
1.0619
2.9713
20
1.0439
3-4833
1 .0496
3.2921
1-0556
3.1217
1.0620
2.9689
19
1 .0440
3-4799
1.0497
3-2891
I-0557
3-1190
1.0622
2.9665
18
1. 044 1
3-4766
1.0498
3.2861
1-0558
3-1163
1.0623
2.9641
17
1.0442
3-4732
1.0499
3-2831
1-0559
3-1137
1.0624
2.9617
16
1 .0443
3-4698
1.0500
3-2801
1 .0560
3.1110
1.062 s
2.9593
IS
1.0444
3.4665
1.0501
3-2772
1.0561
3.1083
1-0626
2.9569
14
1.0445
3-4632
1.0502
3-2742
1.0562
3.1057
1.0627
2.9545
13
1 .0446
3-4598 :
1-0503
3.2712
1-0563
3-1030
1.0628
2.9521
12
1.0447
3-4565
1.0504
3-2683
1-0565
3.1004
1.0629
2.9497
II
1 .0448
3-4532
1.0505
3-2653
1.0566
3-0977
1.0630
2.9474
10
1.0448
3-4498
1.0506
3-2624
1.0567
3-0951
1.0632
2.9450
9
1.0449
3-4465
1.0507
3-2594
1.0568
3-0925
1.0633
2.9426
8
1.0450
3-4432
1.0508
3-2565
1.0569
3-0898
1-0634
2.9402
7
1. 045 1
3-4399
1.0509
3.2535
1.0570
3-0872
1-0635
2-9379
6
1.0452
3-4366
1.05 10
3.2506
1.0571
3.0846
1.0636
2-9355
5
I -0453
3-4334
1-051I
3-2477
1.0572
3.0820
1-0637
2.9332
4
1.0454
3-4301
1.0512
3-2448
1.0573
3-0793
1-0638
2.9308
3
1 .0455
3-4268
1-0513
3-2419
I.0574
3.0767
1-0639
2-9285
2
1.0456
3-4236
1.05 14
3-2390
1.0575
3-0741
1-0641
2-9261
I
1.0457
3-4203
1-0515
3-2361
1.0576
3.0715
1.0642
29238
0
Co-sec.
Sec.
Co-sec.
Sec.
Co-SEC.
Sec.
Co-SEC.
Sec.
/
7c
»^
72
1
71
° 1
7C
P
NATURAL SECANTS AND CO-SECANTS
557
20°
21°
22°
23°
'
Sec.
Co-sec.
Sec.
CO-SEC.
Sec.
Co-sec.
Sec.
Co-sec.
f
o
1.0642
2.9238
1.0711
2.7904
1.078s
2.669s
1.0864
2.5593
6c
I
1-0643
2.9215
1.0713
2.7883
1.0787
2.6675
1.0865
2.5575
55
2
1.0644
2.9191
1.0714
2.7862
1.0788
2.6656
1.0866
2.5558
5^
3
1.0645
2.9168
1.0715
2.7841
1.0789
2.6637
1 .0868
2.5540
57
4
1.0646
2.9145
1.0716
2.7820
1.0790
2.66i8
1.0869
2.5523
5C
5
1.0647
2.9122
1.0717
2.7799
1.0792
2.6599
1.0870
2.5506
55
6
1.0648
2.9098
1.0719
2.7778
1.0793
2.6580
1.0872
2.5488
54
7
1.0650
2.9075
1.0720
2.7757
1.0794
2.6561
1.0873
2.5471
53
8
1. 065 1
2.9052
1. 072 1
2.7736
1 .0795
2.6542
1.0874
2.5453
52
9
1.0652
2.9029
1.0722
2.7715
1.0797
2.6523
1.0876
2.5436
51
lO
1.0653
2.9006
1.0723
2.7694
1.0798
2.6504
1.0877
2.5419
50
II
1.0654
2.8983
1.0725
2.7674
1.0799
2.6485
1.0878
2.5402
49
12
1.065s
2.8960
1.0726
2./653
i.oSoi
2.6466
1.0880
2.5384
48
13
1.0656
2.8937
1.0727
2.7632
1.0802
2.6447
1.0881
2.5367
47
14
1.0658
2.8915
1.0728
2.7611
1.0803
2.6428
1.0882
2.5350
46
IS
1.0659
2.8892
1.0729
2.7591
1.0804
2.6410
1.0884
2-5333
45
i6
1.0660
2.8869
1.0731
2.7570
1.0806
2.6391
1.0885
2.5316
44
17
1. 066 1
2.8846
1.0732
2.7550
1.0807
2.6372
1.0886
2.5299
43
i8
1.0662
2.8824
1 .0733
2.7529
1.0808
2.6353
1.0888
2.5281
42
19
1.0663
2.8801
1.0734
2.7509
: 1. 08 10
2.6335
1.0889
2.5264
41
20
1.0664
2.8778
1.0736
2.7488
1.0811
2.6316
1. 089 1
2.5247
40
21
1.0666
2.8756
I.0737
2.7468
I.0812
2.6297
1 .0892
2.5230
39
22
1.0667
2.8733
1.0738
2.7447
1.0813
2.6279
1.0893
2.5213
38
23
1.0668
2.8711
I.0739
2.7427
1.0815
2.6260
1 .0895
2.5196
37
24
1.0669
2.8688
1.0740
2.7406
1. 08 16
2.6242
1.0896
2.5179
36
25
1.0670
2.8666
1.0742
2.7386
1.0817
2.6223
1.0897
2.5163
35
26
1. 067 1
2.8644
1.0743
2.7366
1.0819
2.6205
1.0899
2.5146
34
27
1.0673
2.8621
1.0744
2.7346
1.0820
2.6186
1.0900
2.5129
33
28
1.0674
2.8599
1.0745
2.7325
1.0821
2.6168
1.0902
2.5112
32
29
1.067s
2.8577
1.0747
2.7305
1.0823
2.6150
1.0903
2.5095
31
30
1.0676
2.8554
1.0748
2.7285
1.0824
2.6131
1.0904
2.5078
30
31
1.0677
2.8532
1.0749
2.7265
1.0S25
2.6113
1.0906
2.5062
29
32
1.0678
2.8510
1.0750
2.7245
1.0826
2.6095
1.0907
2.504s
28
33
1.0679
2.8488
1.0751
2.7225
1.0828
2.6076
1.0908
2.5028
27
34
I. 068 I
2.8466
I.0753
2.7205
1.0829
2.6058
1. 0910
2.5011
26
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1.0682
2.8444,
1.0754
2.7185
1.0830
2.6040
1. 091 1
2.4995
25
36
1.0683
2.8422
1.075S
2.7165
1.0832
2.6022
1.0913
2.4978
24
37
1.0684
2.8400
1.0756
2.7145
1.0833
2.6003
1.0914
2.4961
23
38
1.06S5
2.8378
1.0758
2.7125
1-0834
2.5985
1.0915
2.4945
22
39
1.0686
2.8356
1 .0759
2.7105
1.0836
2.5967
1.0917
2.4928
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1.0688
2.8334
1.0760
2.7085
1.0837
2.5949
1.0918
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1.0689
2.8312
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2.5931
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1 .0690
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1.0763
2.7045
1.0840
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2.8269
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1.0922
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17
M
1.0692
2.8247
1.0765
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1.0842
2.5877
1.0924
2.4846
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1.0694
2.8225
1.0766
2.6986
1.0844
2.5859
1.0925
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15
J6
1.0695
2.8204
1.0768
2.6907
1.0845
2.5841
1.0927
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14
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1.0696
2.8182
1.0769
2.6947 1
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2.5823
1.0928
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1.0697
2.8160
1.0770
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1.0847
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1.0929
2.4780
12
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1.0698
2.8139
1.0771
2.6908
1.0849
2.5787
1.0931
2.4764
11
0
1.0699
2.8117
1.0773
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2.5770
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2.8096
1.0774
2.6869 i
1. 085 1
2.5752
1.0934
2.4731
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2
1.0702
2.8074
1.0775
2.6849
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2.5734
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2.4715
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3
1.0703
2.8053
1.0776
2.6830
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2.5716
1.0936
2.4699
7
4
1.0704
2.8032
1.0778
2.6810
1.0855
2.5699
1.0938
2.4683
6
5
1. 0705
2.8010
1.0779
2.6791
1.0857
2.56S1
1.0939
2.4666
5
6
1.0707
2.7989
1.0780
2.6772
1.0858
2.5663
1.0941
2.4650
4
7
1.0708
2.7968
1. 078 1
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1.0859
2.5646
1 .0942
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3
8
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2.7947
1.0783
2.6733 !
1. 086 1
2.5628
1.0943
2.4618
2
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2.7925
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2.6714
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1.0711
2.7904
1.0785
2.6695 :
1.0864
2.5593
1 .0946
Co-sec.
2.4586
0
/
Co-sec.
Sec.
CO-SEC.
Sec
Co-sec.
Sec.
Sfp,
"7"
69
0
6S
0
67
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66
°
558
NATURAL SECANTS AND CO-SECANTS
24°
25° !
26° 1
27° 1
Sec.
Co-sec.
Sec.
Co-SEC.
Sec.
Co-SEC.
Sec.
Co-SEC.
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1.0946
2.4586
1. 1034
2.3662
1. 1126
2.2812
1.1223
2.2027
60
1.0948
2.4570
1.I035
2.3647
1.1127
2.2798
1.1225
2.2014
59
1.0949
2.4554
1. 1037
2.3632
1.1129
2.2784
1. 1226
2.2002
58
1. 095 1
2.4538
1.1038
2.3618
1.1131
2.2771
1.1228
2.1989
57
1.0952
2.452-'
I. 1040
2.3603
1.1132
2.2757
1.1230
2.1977
56
10953
2.4506
1.1041
2.3588
i.iiU
2.2744
1. 1231
2.1964
55
I-0955
2.4490
1.1043
2-3574
I.1I35
2.2730
1.1233
2.1952
54
1.0956
2.4474
1.1044
2.3559
1.1137
2.2717
1.1235
2.1939
53
1.0958
2.4458
1.1046
2.3544
1.1139
2.2703
1. 1237
2.1927
52
1.0959
2.4442
1.1047
2.3530
1. 1140
2.2690
I.1--38
2.1914
51
1. 096 1
2.4426
1.1049
2.3515
1. 1142
2.2676
1.1240
2.1902
50
1.0962
2.4411
I. 1050
2.3501
1. 1143
2.2663
1. 1242
2.1889
49
1.0963
2.4395
1.1052
2.3486
1.1145
2.2650
1.1243
2.1877
48
1.0965
2-4379
1.1053
2.3472
1.1147
2.2636
1.1245
2.1865
47
1.0966
2.4363
1.1055
2.3457
1.1148
2 2623
I. 1247
2.1852
46
1.0968
2.4347
1.1056
2.3443
1.1150
2.2610
1.1248
2.1840
45
1.0969
2.4332
1. 1058
2.3428
1.1151
2.2596
1.1250
2.1828
44
1. 097 1
2.4316
1.1059
2-3414
I.I153
2.2583
1.1252
2.1815
43
1.0972
2.4300
1. 1061
2-3399
I-1I55
2.2570
1.1253
2.1803
42
1.0973
2.4285
1.1062
2.3385
1.1156
2.2556
1.1255
2.1791
41
I.0975
2.4269
1. 1064
2.3371
1.1158
2.2543
1.1257
2.1778
40
1.0976
2.4254
1.1065
2.3356
1.1159
2.2530
1. 1258
2.1766
39
1.0978
2.4238
1.1067
2.3342
1.1161
2.2517
1.1260
2.1754
38
1.0979
2.4222
1.1068
2.3328
1.1163
2.2503
1.1262
2.1742
37
1.0981
2.4207
1.1070
2.3313
1.1164
2.2490
1.1264
2.1730
36
1.0982
2.4191
1.1072
2.3299
1.1166
2.2477
1.1265
2.1717
35
1.0984
• 2.4176
1.1073
2.3285
1.1167
2.2464
I. 1267
2.170s
34
1.0985
2.4160
I. 1075
2.3271
1.1169
2.2451
1.1269
2.1693
33
1.0986
2.4145
1.1076
2.3256
1.1171
2.2438
1.1270
2.1681
32
1.0988
2.4130
1.1078
2.3242
1.1172
2.2425
1.1272
2.1669
51
1.0989
2.41 14
1.1079
2.3228
1.1174
2.2411
1. 1274
2.1657
30
1.0991
2.4099
1.1081
2.3214
T.1176
2.2398
I.127S
2.1645
29
1.0992
2.4083
1.1082
2.3200
1.1177
2.2385
1.1277
2.1633
28
1.0994
2.4068
1.1084
2.3186
1.1179
2.2372
1.1279
. 2.1620
27
1.0995
2.4053
1.1085
2.3172
1.1180
2.2359
1.1281
2.1608
26
1.0997
2.4037
1. 1087
2.3158
1.1182
2.2346
1.1282
2.1596
25
1.099S
2.4022
1.1088
2.3143
1.1184
2.2333
1.1284
2.1584
24
l.IOOO
2.4007
1.1090
2.3129
1.1185
2.2320
1.12S6
2.1572
23
l.IOOI
2.3992
1.1092
2.3115
1. 1187
2.2307
1.1287
2.1560
22
1.1003
2.3976
1.1093
2.3101
1.1189
2.2294
1. 1289
2.1548
21
1.1004
2.3961
1.109s
2.3087
I. 1190
2.2282
1.1291
2.1536
20
1. 1005
2.3946
1.1096
2.3073
1.1192
2.2269
1.1293
2.1525
19
1.1007
2.3931
1.1098 .
2.3059
1.1193
2.2256
1.1294
2.1513
18
1.1008
2.3916
1.1099
2.3046
1.1195
2.2243
1.1296
2.1501
17
1. 1010
2.3901
I.IIOI
2.3032
1.1197
2.2230
1.1298
2.1489
16
l.lOll
2.3S86
1. 1102
2.3018
1.1198
2.2217
I. 1299
2.1477
15
I.IOI3
2.3871
1. 1104
2.3004-
1. 1200
2.2204
1. 1301
2.1465
14
1.1014
2.3856
1. 1106
2.2990
1.1202
2.2192
1.1303
2.1453
13
I. 1016
2.3841
1.1107
2.2976
1.1203
2.2179
1.1305
2.1441
12
1.IOI7
2.3826
1.1109
2.2962
1.1205
2.2166
I. 1306
2.1430
II
I. 1019
2.3811
I. 1110
2.2949
1.1207
2.2153
1.1308
2.1418
10
1.I02C
2.3796
I. 1112
2.2935
1.1208
2.2141
1.1310
2.1406
9
I 1022
2.3781
1.1113
2,2921
I 1210
2.2128
1. 1312
2.1394
8
I. 1023
2.3766
l.iiiS
2.2907
1.1212
2.2115
1.1313
2.1382
7
1. 1025
2-3751
1.1116
2.2894
1.1213
2.2103
1.131s
2.1371
6
1. 1026
2.3736
1.1118
2.2880
1.1215
2.2090
1.1317
2.1359
5
1. 1028
2.3721
1.1120
2.2866
1.1217
2.2077
1.1319
2.1347
4
1.1029
2.3706
1.1121
2.28«;3
1. 1218
2.2065
1.1320
2.133s
3
1. 1031
2.3691
I.1123
2.2839
1.1220
2.2052
1. 1322
2.1324
2
1.1032
2.3677
1. 1124
2.2825
1. 1222
2.2039
1.1324
2.1312
I
1.1034
2.3662
1.1126
2.2812
1.1223
2.2027
1.1326
2.1300
0
Co-sec.
Sec.
Co-SEC.
Sec.
Co-SEC
Sec.
Co-SEC.
Sec
•
6.
)°
i 6^
1°
6;
J°
6^
JO
NATURAL SECANTS AND CO-SECANTS
559
28°
29° 1
#
Sec.
Co-SEC.
Sec.
Co-SEC.
o
I. 1326
2.1300
I.I433
2.0627
I
1.1327
2.1289
1.1435
2.0616
2
1.1329
2.1277
1.1437
2.0605
3
1.1331
2.1266
1.1439
2.0594
4
I.I333
2.1254
1.1441
2.0583
5
1.1334
2.1242
1.1443
2.0573
6
1. 1336
2.1231
1.1445
2.0562
7
1.1338
2.1219
1.1446
2-0551
8
1.1340
2.1208
1.1448
2.0540
9
1.1341
2.1 196
1.1450
2.0530
lO
1.1343
2.1185
1.1452
2.0519
II
I.1345
2.1173
1.1454
2.0508
12
1.1347
2.1162
1.1456
2.0498
13
1. 1349
2.1150
1.1458.
2.0487
14
1.1350
2.1139
1.1459
2.0476
15
1.1352
2.1127
1. 1461
2.0466
i6
1-1354
2.1116
1.1463
2-0455
17
1.1356
2.1104
1.1465
2.0444
i8
1.1357
2.1093
1.1467
2.0434
19
1.1359
2.1082
1.1469
2.0423
20
1.1361
2.1070
1.1471
2-0413
21
1.1363
2.1059
1.1473
2.0402
22
1.1365
2.1048
1.1474
2.0392
23
1. 1 366
2.1036
1.1476
2.0381
24
1.1368
2.1025
1.1478
2.0370
25
1.1370
2.1014
I. 1480
2.0360
26
1.1372
2.1002
1.1482
2.0349
27
1.1373
2.0991
1.1484
2.0339
28
1.1375
2.0980
1.1486
2.0329
29
1.1377
2.0969
1.1488
2.0318
3°
1.1379
2.0957
1.1489
2.0308
31
1.1381
2.0946
1.1491
2.0297
32
1.1382
2.0935
1.1493
2.0287
33
1.1384
2.0924
X.1495
2.0276
34
1. 1 386
2.0912
1.1497
2.0266
35
1.1388
2.0901
1.1499
2.0256
36
1.1390
2.0890
1.1501
2.0245
37
1.1391
2.0879
^.1503
2.023s
38
1.1393
2.0868
1.1505
2.0224
39
1.1395
2.0857
1.1507
2.0214
40
1.1397
2.0846
1.1508
2.0204
41
1.1399
2.0835
1. 1510
2.0194
42
1.1401
2.0824
1.1512
2.0183
43
I. 1402
2.0812
1.1514
2.0173
44
I. 1404
2.0801
1.1516
2.0163
45
I. 1406
2.0790
1.1518
2.0152
46
1. 1 408
2.0779
1.1520
2.0142
47
1.1410
2.0768
I.J522
S.O132
48
1.1411
2.0757
1.1524
2.0122
49
1.1413
2.0746
1.1526
2.0I1I
SO
1.1415
2.0735
I.I528
2.0101
51
1.1417
2.0725
1.1530
2.0091
52
1. 1419
2.0714
1.1531
2.0081
53
1.1421
2.0703
1.1533
2.0071
54
1. 1422
2.0692
1. 1535
2.0061
55
1.1424
2.0681
I.I537
2.0050
56
I. 1426 .
2.0670
1.1539
2.0040
H
1. 1428
2.0659
1.1541
2.0030
58
1.1430
2.0648
1.1543
2.0020
59
1.1432
2.0637
1.1545
2.0010
60
1.1433
2.0627
1.1547
2.0000
f
Co-SEC.
Sec.
Co-SEC.
Sec.
6]
L°
6(
r
30°
Sec. Co-SEC.
1547
1549
1551
1553
1555
1557
1559
1561
1562
1564
1566
1568
1570
1572
1574
1576
1578
1580
1582
1584
1586
1588
1590
1592
1594
1596
1598
1600
1602
1604
1606
1608
1610
1612
1614
1616
1618
1620
1622
1624
1626
1628
1630
1632
1634
1636
1638
1640
1642
1644
1646
1648
1650
1652
1654
1656
1658
1660
1662
1664
1666
0000
9990
9980
9970
9960
9950
9940
9930
9920
9910
9900
9890
9880
9870
9860
9850
9840
9830
98 20
98 1 1
.9801
9791
9781
9771
9761
9752
9742
9732
.9722
9713
9703
9693
9683
9674
9664
9654
9645
9635
9625
9616
9606
9596
9587
9577
9568
9558
9549
9539
9530
9520
9510
9501
9491
.9482
9473
9463
■9454
9444
9435
■9425
,9416
Co-SEC. Sec.
69°
31°
Sec. Co-sec.
1666
1668
1670
1672
1674
1676
1678
1681
1683
1685
1687
1689
1 691
1693
1695
1697
1699
1701
1703
1705
1707
1709
1712
1714
1716
1718
1720
1722
1724
1726
1728
1730
1732
1734
1737
1739
1741
1743
1745
1747
1749
1751
1753
1756
1758
1760
1762
1764
1766
1768
1770
1772
1775
1777
1779
1781
1783
1785
1787
1790
1792
1.9416
9407
9397
93S8
9378
9369
.9360
9350
9341
9332
9322
9313
9304
9295
.9285
,9276
,9267
9258
9248
9239
9230
9221
9212
9203
9193
9184
9175
9166
9157
9148
9139
9130
9121
9112
9102
9093
9084
9075
9066
9057
9048
9039
9030
9021
9013
9004
8905
S986
8977
8968
8959
8950
8941
8932
8924
8915
8906
8897
8888
8S79
8871
Co-sec. Sec.
58=
56o
NATURAL SECANTS AND CO-SECANTS
32
0
32
°
34° I
35°
'
Sec.
Co-sec.
Sec.
Co-sec.
Sec.
Co-SEC.
Sec.
Co-SEC.
t
o
1.1792
1. 887 1
1.1924
1.8361
1.2062
1.7883
1.2208
1.7434
60
I
I. 1794
1.8862
1.1926
1.8352
1.2064
1.787s
1.2210
1.7427
59
2
1.1796
1.8853
1.1928
1-8344
1.2067
1.7867
1.2213
1.7420
58
3
1.1798
1.S844
1. 1930
1.8336
1.2069
1.7860
1.2215
1.7413
57
4
1. 1800
1.8836
1.1933
1.8328
1.2072
1.7852
1.2218
1.7405
56
5
1.1802
1.8827
I. 1935
1.8320
1.2074
1.7844
1.2220
1.7398
55
6
1.1805
1.8818
1.1937
1.8311
1.2076
1.7837
1.2223
1.7391
54
7
1.1807
1.8S09
1-1939
1.8303
1.2079
1.7829
1.2225
1.7384
53
8
1.1809
1.8801
1.1942
1.8295
1.2081
1.7821
1.2228
1.7377
52
9
1.1811
1.8792
1.1944
1.8287
1.2083
1.7814
1.2230
1.7369
51
lO
1.1813
1.8783
1. 1 946
1.8279
1.2086
1.7806
1.2233
1.7362
50
11
1.1815
1.8785
1.1948
1.8271
1.2088
1.7798
1-2235
1.7355
49
12
1.1818
1.8766
1.T951
1.8263
1.2091
1.7701
1.2238
1.7348
48
13
1.1820
1-8757
1-1953
1-8255
1.2093
•1.7783
1.2240
1.7341
47
14
1.1822
1.8749
1-1955
1.8246
1.2095
1.7776
1-2243
1.7334
46
15
1.1824
1.8740
1-1958
1.8238
1.2098
1.7768
1.2245
1.7327
45
i6
1.1826
1-8731
1.1960
1.8230
1.2100
1.7760
1.2248
1-7319
44
17
1.1828
1.8723
1.1962
1.8222
1.2103
1.7753
1.2250
I.7312
43
i8
1.1831
1.8714
1. 1 964
1.8214
1.2105
1.774s
1.2253
1-7305
42
19
1-1833
1.8706
1.1967
1.8206
1.2107
1.7738
1-2255
1.7298
41
20
1-1835
1.8697
1.1969
1.8198
1.2110
1.7730
1.2258
1.7291
40
21
1.1837
1.8688
1. 1971
1.8190
1.2112
1.7723
1.2260
1.7284
39
22
1.1839
1.8680
1.1974
1.8182
1.2115
1.7715
1.2263
1.7277
38
2Z
1.1841
1.8671
1.1976
1.8174
1.2117
1.7708
1.2265
1.7270
37
24
1.1844
1.8663
1.1978
1.8166
1.2119
1.7700
1.2268
1.7263
36
25
1.1846
1.8654
1.1980
1.8158
1.2122
1.7693
1.2270
1.7256
35
26
1.1848
1.8646
1.1983
1.8150
1.2124
1.7685
1-2273
1-7249
34
27
1.1850
1.8637
1.198s
1.8142
1.2127
1.7678
1.2276
1.7242
33
28
1.1852
1.8629
1.1987
1.8134
1.2129
1.7670
1.2278
1-7234
32
29
1-1855
1.8620
1.1990
1.8126
1.2132
1.7663
I.228I
1.7227
31
30
1-1857
1.8611
1.1992
1.8118
1.2154
1.765s
1.2283
1.7220
30
31
1-1859
1.8603
1-1994
1.8110
1.2136
1.7648
1.2286
1.7213
29
32
1.1861
1-8595
1.1997
1.8102
1.2139
1.7640
1.2288
1.7206
28
33
1.1863
1.8586
1.1999
1.8094
1.2141
1.7633
1.2291
1.7199
27
34
1.1866
1.8578
1.2001
1.8086
1.2144
1.7625
1.2293
1.7192
26
35
1.1868
1.8569
1.2004
1.8078
1.2146
1.7618
1.2296
1.7185
25
36
1.1870
1.8561
1.2006
1.8070
1.2149
1. 7610
1.2298
1-7178
24
37
1.1872
1.8552
1.2008
1.8062
1.2151
1.7603
1.2301
1.7171
23
38
1.1874
1.8544
1.2010
1.8054
1.2153
1-7596
1.2304
1.7164
22
39
1.1877
1.8535
1.2013
1.8047
1.2156
1.7588
1.2306
1.7157
21
40
1.1879
1.8527
1.2015
1-8039
1.2158
1.7581
1.2309
1.7151
20
41
1.1881
1.8519
1.2017
1.8031
I.2161
1.7573
1.2311
1.7144
'2
42
1.1883
1.8510
1.2020
1.8023
1.2163
1.7566
1.2314
1.7137
18
43
1.1886
1.8502
1.2022
1.8015
1.2166
1.7559
1.2316
1.7130
17
44
1.1888
1.8493
1.2024
1.8007
1.2168
1.7551
1.2319
1.7123
16
45
1.1890
1.8485
1.2027
1-7999
1.2171
1.7544
1.2322
1.7110
15
46
1.1892
1.8477
1.2029
1.7992
1-2173
1.7537
1.2324
1.7109
14
47
1.1894
1.8468
1.2031
1.7984
1.2175
i-75«9
1.2327
1.7102
13
48
1.1897
1.8460
1.2034
1.7976
1.2178
1-7522
i.2329
^•'°25
12
49
1.1899
1.8452
1.2036
1.7968
1. 2 180
1-7514
1.2332
1.7088
11
50
l.IOOI
1-8443
1.2039
1.7960
1.2183
1-7507
1.2335
1.7081
10
51
1.1903
1-8435
1.2041
1-7953
^■^'ll
1-7500
1.2337
1.707s
I
52
1.1906
1.8427
1.2043
1-7945
1. 2 188
1-7493
1.2340
1.7068
8
53
1.1908
1. 8418
1.2046
1-7937
1.2190
1-7485
1.2342
1.7061
7
54
1.1910
1. 84 10
1.2048
1.7929
1.2193
1.7478
1.2345
1-7054
6
55
1.1912
1.8402
1.2050
1.7921
1.2195
1-7471
1.2348
1.7047
5
56
1.I9I5
1.8394
1-2053
1.7914
1.2198
1-7463
1-2350
1.7040
4
57
1.1917
1-8385
1.2055
1.7906
1.2200
1-7456
1.2353
1-7033
3
58
1.1919
1-8377
1.2057
1.7898
1.2203
1.7449
1-2355
1.7027
2
59
I. 1921
1.8369
1.2060
1.7891
1.2205
1.7442
1.2358
1.7020
1
60
I. 1922
1.8361
1.2062
1.7883
1.2208
1-7434
1.2361
1-7013
0
t
Co-sec.
Sec.
Co-sec.
Sec.
Co-SEC.
Sec.
Co-SEC.
Sec
'^
5
7c
1 5
6°
5
5°
1 5
40
NATURAL SECANTS AND CO-SECANTS
561
36
0
37
0
3S
0
sg
0
Sec.
Co-SEC.
Sec.
Co-SEC.
Sec.
Co-SEC.
Sec.
Co-SEC.
/
1.2361
1. 7013
1.2521
1. 6616
1.2690
1.6243-
1.2867
1.5890
60
1.2363
1.7006
1.2524
1.6610
1-2693
1.6237
1.2871
1.5884
59.
1.2366
1.6999
1.2527
1.6603
1.2696
1.6231
1.2874
1-5879
58
1.2368
1.6993
1.2530
1.6597
1.2699
1.6224
1.2877
1-5873
57
1.2371
1.6986
1.2532
1.6591
1.2702
1.6218
1.2880
1.5867
S6
1-2374
1.6979
1-2535
1.6584
1-2705
1.6212
1.2883
1.5862
55
1.2376
1.6972
1-2538
1.6578
1.2707
1.6206
1.2886
1.5856
54
1.2379
1.6965
1-2541
1.6572
1.2710
1.6200
1.2889
1.5850
S3
1.2382
1.6959
1-2543
1.6565
1.2713
1.6194
1.2892
1.5845
52
1.2384
1.6952
1.2546
1.6559
1.2716
1.6188
1-2895
1-5839
51
1.2387
1.694s
1.2549
1.6552
1.2719
1.6182
1.2898
1-5833
50
1.2389
1.6938
1.2552
1.6546
1.2722
1. 61 76
1.2901
1.5828
49
1.2392
1.6932
1.2554
1.6540
1-2725
1.6170
1.2904
1.5822
48
1-2395
1.6925
1.2557
1.6533
1.2728
1.6144
1.2907
1.5816
47
1.2397
1. 6918
1.2560
1.6527
1.2731
1.6159
1.2910
1.5811
46
1.2400
1. 691 2
1.2563
1.6521
1-2734
1-6153
1.2913
1.580s
45
1.2403
1.6905
1.2565
1.6514
1-2737
1.6147
1.2016
1.5799
44
1.2405
1.6898
1.2568
1.6508
1.2739
1.6141
1.2919
1-5794
43
1.2408
1. 689 1
1.2571
1.6502
1-2742
1-6135
1.2922
1.5788
42
1.2411
1.688 s
1-2574
1.6496
1-2745
1.6129
1.2926
1.5783
41
1-2413
1.687S
1-2577
1.6489
1.2748
I.6123
1.2929
1.5777
40
1.2416
1. 6871
1.2579
1.6483
1.2751
I.6117
1.2932
I.5771
39
1.2419
1.6865
1.2582
1.6477
1.2754
1.6111
1.2935
1-5766
38
1.2421
1.6858
1.2585
1.6470
1.2757
1.6105
1.2938
1.5760
37
1.2424
1. 685 1
1.2588
1.6464
1.2760
1.6099
1.2941
1-5755
36
1.2427
1.6845
1.2591
1.6458
1.2763
1-6093
1.2944
1-5749
35
1.2429
1.6838
1.2593
1.6452
1.2766
I.60S7
1.2947
1-5743
34
1.2432
1. 683 1
1.2596
1.6445
1.2769
1.6081
1.2950
1.5738
33
1.2435
1.6825
1.2599
1.6439
1.2772
1.6077
1-2953
1-5732
32
1.2437
1. 68 18
1.2602
1.6433
1.2775
1.6070
1.2956
1.5727
31
1.2440
1.6812
1.260s
1.6427
1.2778
1.6064
1.2960
1.5721
30
1.2443
1.6805
1.2607
1.6420
1.2781
1.6058
1.2963
1.5716
2g
1.2445
1.6798
1. 2610
1.6414
1.2784
1.6052
1.2966
1.5710
28
1.2448
1.6792
1.2613
1.6408
1.2787
1.6046
1.2969
1-5705
27
1.2451
1.6785
1.2616
1.6402
1.2790
1 .6040
1.2972
1.5699
26
1.2453
1.6779
1. 2619
1.6396
1.2793
1.6034
1-2975
1.5694
25
1.2456
1.6772
1.2622
1.6389
1.2795
1.6029
1.2978
1.5688
24
I.24S9
1.6766
1.2624
1.6383
1.2798
1.6023
1.2981
1-5683
23
1. 2461
1.6759
1.2627
1.6377
1.2801
1.6017
1-2985
1-5677
22
1.2464
1.6752
1.2630
1.6371
1.2804
1.6011
1.2988
1.5672
21
1.2467
1.6746
1.2633
1.6365
1.2807
1. 6005
I.2991
1.5666
20
1.2470
1.6739
1.2636
1-6359
1. 2810
1 .6000
1.2994
1.5661
19
1.2472
1.6733
1.2639
1-6352
1-2813
1.5994
1.2997
1-5655
18
1.2475
1.6726
1.2641
1-6346
1.2816
1.5988
. 1.3000
1-5650
17
1.2478
1.6720
1.2644
1.6340
1.2S19
1-5982
1-3003
1.5644
i6
1.2480
1.6713
1.2647
1-6334
1.2822
1.5976
1.3006
1-5639
15
1.2483
1.6707
1.2650
1.6328
1.2825
I.5971
1.3010
1-5633
14
1.2486
1.6700
1.2653
1.6322
1.2828
1.5965
1-3013
1.5628
13
1.2488
1.6694
1.2656
1.6316
1.2831
1.5959
1.3016
1.5622
12
1.2490
1.6687
1.2659
1.6309
1.2834
1.5953
1.3019
1-5617
11
1.2494
1. 668 1
1.2661
1.6303
1.2837
1.5947
1.3022
1.561 1
10
1.2497
1.6674
1.2664
1.6297
1.2840
1.5942
1-3025
1.5606
9
1.2499
1.6668
1.2667
1.6291
1.2843
1.5936
1-3029
1.5600
8
1.2502
1. 666 1
1.2670
1.6285
1.2846
1.5930
1-3032
1.5595
I
1-2505
1.6655
1.2673
1.6279
1.2849
1.5924
1-3035
1.5590
1.2508
1.6648
1.2676
1.6273
1.2852
1.5919
1-3038
1-5584
S
.1.2510
1.6642
1.2679
1.6267
1.2855
I -59 1 3
1.3041
1-5579
4
1.2513
1.6636
1.2681
1.6261
1.2858
1-5907
1.3044
1-5573
3
1.2516
1.6629
1.2684
1-6255
1.2861
1-5901
1.3048
1-5568
2
1.2519
1.6623
1.2687
1.6249
1.2864
1-5896
1-3051
1-5563
I
1.2521
1.6616
1.2690
1.6243
1.2867
1-5890
1-3054
1.5557
0
Co-SEC.
Sec.
Co-SEC.
Sec.
Co-SEC.
Sec.
Co-SEC
Sec,
/
6
3°
6
20
d
1«
1 6
0°
NATURAL SECANTS AND CO-SECANTS
40°
Sec. Co-sec.
1-3054
1-3057
1 .3060
1.3064
1.3067
1.3070
1-3073
1.3076
1.3080
1-3083
1.3086
1 .3089
1.3092
1.3096
1.3099
1.3102
1-3105
1. 3109
1.3112
1-3115
1.3118
1.3121
1-3125
1.3128
1.3131
1-3134
I.. ^38
1.3141
1.3144
1.3148
1.3151
1.3154
1.3157
1.3161
1.3164
1.3167
1.3170
1.3174
1.3177
1.3180
1.3184
1.3187
1.3190
1-3193
1-3197
1.3200
1-3203
1.3207
1.3210
1-3213
1.3217
1.3220
1-3223
1.3227
1.3230
1.3233
1.3237
1.3240
1.3243
1.3247
1.3250
CO-SF.C,
1-5557
1-5552
1.5546
1.5541
1.5536
1-5530
1-5525
1-5520
1-5514
1-5509
1.5503
1.5498
1 5403
1.5487
1.5482
1-5477
1-5471
1.5466
1.5461
1.5456
1.5450
1-5445
1.5440
1.5434
1.5429
1.5424
1.5419
1.5413
1.5408
1.5403
1.5398
1.5392
1.5387
1.5382
1.5377
1.5371
1.5366
1.5361
1.5356
1-5351
1.5345
1.5340
1.5335
1.5330
1.5325
1-5319
1.5314
1.5309
1.5304
1.5299
1-5294
1.5289
1-5283
1.5278
1-5273
1.5268
1.5263
1.5258
1.5253
1.5248
1.5242
Sec.
41
Sec. Co-sec.
49'
1.3250
1.3253
1.3257
1.3260
1-3263
1.3267
1.3270
1-3274
1-3277
1.3280
1.3284
1.3287
1.3290
-4.3294
1.3297
1.3301
1.3304
1.3307
1.3311
1-3314
1-3318
1-3321
1.3324
1.3328
1.3331
1.3335
1.3338
1.3342
1-3345
1.3348
1-3352
1-3355
1-3359 •
1.3362
1.3366
1.3369
1.3372
1-3376
1-3379
1.3383
1.3386
I-3390
1-3393
1-3397
1-3400
1-3404
1.3407
1.3411
1.34M
1.3418
1.3421
1.3425
1.3428
1.3432
1-3435
1-3439
1.3442
1.3446
1-3449
1.3453
1.3456
Co-sec.
1.5242
1.5237
1.5232
1.5227
1.5222
1.5217
1.5212
1.5207
1.5202
1.5197
1.5192
1.5187
1.5182
1.5177
1.5171
1.5166
1.5161
1-5156
1-5151
1.5146
1.5141
1-5136
1-5131
1.5126
1.5121
1.5116
1.5111
1.5106
1.5101
1.5096
1.5092
1.5087
1.5082
1.5077
1-5072
1.5067
1.5062
1-5057
1-5052
1-5047
1.5042
1.5037
1.5032
1.5027
1-5022
1.5018
1-5013
1 .5008
1.5003
1.4998
1-4993
1.4988
1.4983
1.4979
1.4974
1.4969
1.4964
1-4959
1-4954
1.4949
1-4945
Sec.
48=
42° 11
43°
Sec.
Co-sec.
Sec.
Co-sec.
t
1.3456
1.4945
1.3673
1.4663
60
1.3460
1.4940
1.3677
1.4658
59
1.3463
1.4935
1.3681
1.4654
58
1.3467
1.4930
1.3684
1.4649
57
1.3470
1.4925
1.3688
1 .4644
56
1.3474
1.4921
1.3692
1.4640
55
1-3477
1.4916
1.3695
1.4635
54
1.3481
1.4911
1.3699
1.4631
53
1-3485
1.4906
1.3703
1.4626
52
1-3488
1. 490 1
1.3707
1.4622
51
1.3492
1.4897
1.3710
1.4617
50
1-3495
1.4892
1.3714
1.4613
49
1-3499
1.4887
1.3718
1.4608
48
1.3502
1.4882
1.3722
1.4604
47
1.3506
1.4877
1.3725
1.4599
46
1.3509
'•4^73
1.3729
1.4595
45
1.3513
1.4868
1.3733
1.4590
44
I-35I7
1.4863
1.3737
1.4586
43
1.3520
1.4858
1.3740
1.4581
42
1-3524
1.4854
1-3744
1.4577
41
1.3527
1.4849
1.3748
1.4572
40
1.3531
1.4844
1.3752
1.4568
30
1.3534
1.4839
1.3756
1.4563
38
1.3538
1.4835
1.3759
1.4559
37
1.3542
1.4830
1.3763
1.4554
36
1.3545
I.4S25
1.3767
1.4550
35
1.3549
1.4821
1-3771
1-4545
34
1.3552
1.4816
1.3774
1.4541
ZZ
1.3556
1.4811
1.3778
1.4536
32
1.3560
1.4806
1.3782
1.4532
31
1.3563
1.4802
1.3786
1.4527
30
1.3567
1.4797
1.3790
1.4523
29
1.3571
1.4792
1.3794
1.4518
28
1-3574
1.4788
1-3797
1 4514
27
1.3578
1.4783
1.3801
1.4510
26
1.3581
1.4778
1-3805
1-4505
25
1-3585
1.4774
1-3809
1.4501
24-
1-3589
1.4769
1-3813
1.4496
23
1-3592
1.4764
1.3816
1.4492
22
1-3596
1.4760
1.3820
1.4487
21
1.3600
1.4755
1.3824
1-4483
20
1.3603
1.4750
1.3828
1.4479
19
1.3607
1.4746
1-3832
1.4474
18
1.3611
1.4741
1-3836
1.4470
17
1-3614
1.4736
1-3839
1-4465
16
1. 36 1 8
1.4732
1-3843
1.4461
IS
1.3622
1-4727
1-3847
1.4457
14
1-3625
1.4723
1.3851
1.4452
13
1-3629
1.4718
1-3855
1.4448
12
1-3633
1.4713
1-3859
1-4443
11
1-3636
1.4709
1.3863
1-4439
10
1.3640
1.4704
1.3867
1.4435
9
1.3644
1.4699
1.3870
1.4430
8
1..3647
1.4695
1.3874
1.4426
7
1.3651
1 .4690
1.3878
1.4422
6
1.3655
1.4686
1.3882
1.4417
5
1.3658
1. 4681
1.3886
1.4413
4
1.3662
1.4676
1.3890
1.4408
3
1.3666
1.4672
1.3894
1.4404
2
1.3669
1.4667
1.3898
1.4400
I
1.3673
1.4663
1.3902
1-4395
0
Co-sec
Sec.
Co-sec.
Sec.
/
4
70
4
G°
NATURAL SECANTS AND CO-SECANTS
5^3
f
44°
440
440
'
Sec.
Co-SEC.
/
f <
5ec.
Co-SEC.
f
'
Sec
Co-SEC
t
o
1-3902
1-4395
60
21 I
39^4
1-4305
39
41
1-4065
I.4221
19
I
3905
4391
59
22 I
3988
1. 4301
38
42
1-4069
1-4217
18
2
3909
4387
58
23 1
3992
1.4297
H
43
1-4073
I.4212
17
3
3913
4382
57
24 I
3996
^•4292
36
44
I 4077
1.4208
j6
4
3917
4378
56
25 1
4000
1.4288
35
45
1. 408 1
1.4204
15
5
3921
4374
55
26 I
4004
1.4284
34
46
1.4085
1.4200
14
6
3925
4370
54
27 I
4008
1.4280
33
47
1.4089
I.4196
13
7
3929
4365
53
28 I
4012
1.4276
32
48
- 1-4093
I.4192
12
8
3933
4361
52
29 I
4016
I.4271
31
49
1.4097
I.4188
II
9
3937
4357
51
30 I
4020
1.4267
30
50
1.4101
I.4183
10
lO
3941
4352
50
31 I
4024
1-4263
29
51
1.4105
1.4179
9
II
3945
4348
49
32 I
4028
1-4259
28
52
1.4109
I.4175
8
12
3949
4344
48
33 I
4032
1-4254
27
53
1.4113
I.4171
7
13
3953
4339
47
34 r
4036
1-4250
26
54
1.4117
I.4167
6
14
3957
4335
46
35 I
4040
1-4246
25
55
1.4122
I-4163
5
IS
3960
4331
45
36 I
4044
1-4242
24
56
1.4126
I.4159
4
i6
3964
4327
44
37 I
4048
1.4238
23
57
1.4130
1. 41 54
3
17
3968
4322
43
38 I
4052
1-4233
22
58
1.4134
1.4150
2
i8
3972
4318
42
39 I
4056
1.4229
21
59
1.4138
1.4146
I
19
3976
4314
41
40 I
4060
1.4225
20
60
1.4142
1.4142
0
20
3980
1.43 10
40
1
/
Co-SEC.
Sec.
' c
0-SEC.
Sec.
*
[ *
Co-sec
Sec.
"T
4
5°
4
5°
45^
DICTIONARY OF MACHINE SHOP TERMS
This has been compiled to assist in a definite understanding of
the names of tools, appliances and shop terms which are used in
various parts of the country, and will, we trust, prove of value in
this way. Cross references have been used in many cases, and we
believe that no trouble will be experienced in finding the definition
desired even where it may not be under the letter expected. Cutters
of all kinds are under "cutters," twist drills under "drills," and by
bearing this in mind no delay will be experienced. Practical sug-
gestions as to additions to this section will be appreciated.
564
DICTIONARY OF SHOP TERMS
Ampere — The unit of electric current. The amount of current
which one volt can force through a resistance of one ohm.
Ampere Hour. — One ampere flowing for one hour.
Ampere Turns. — Used in magnet work to represent the number of
turns times the number of amperes.
Angle Irons — Pieces, usually castings, for holding work at an angle
with the face-plate of a lathe, the platen of a planer or othei
similar work. Usually at right angles but can be anything
desired.
Angle Plate — A cast-iron plate with two surfaces at right angles to
each other; one side is bolted to a machine table, the other carries
the work.
Annealing — Softening steel, rolled brass or copper by heating to a
low heat and allowing to cool gradually.
Annealing Boxes — Boxes, usually of cast iron, in which steel is
packed with lime or sand to retard the cooling as much as possible.
Anode — The positive terminal of any source of electricity as a bat-
tery, or where the current goes into a plating bath.
Anvils — Blocks of iron or steel on which
metals are hammered or forged. Usu-
ally have a steel face. A square hole
is usually provided for holding hardies,
fuller blocks, etc.
Apron — A protecting or covering piece which encloses or covers any
mechanism, as the apron of a lathe.
Arbor — Shaft or bar to hold work while it is being turned or other-
I — I wise worked on. Usually made with a
b CZ slight taper (about .010 inch per foot) to
*^ drive into work and hold by friction. Also
applied to shaft for holding circular saws, milling cutters, etc.
Often called mandrel.
Arbor, Expansion — Arbor which can be
varied in diameter to hold different
sized work. These vary greatly in
design, as shown. The first and last
are spring sleeves of different types,
the second has blades which can be
adjusted to size.
Arc — The passage of current across the space between two sepa-
rated points.
Armature. — Usually the revolving part of a dynamo or motor or
the movable part of any magnetic device.
565
C
566 BABBITT — BELT
B
Babbitt Metal — A good mixture for bearings where the load is not
too heavy. Consists of varying proportions of tin, antimony,
and copper, and sometimes lead. Tin is the base.
Back-laDh — Usually applied to lost motion in gears, sometimes to
screw in a nut.
Backing-off — Removing metal behind the cutting edge to relieve
friction in taps, reamers, drills, etc. Also called "relieving."
Back Rest — A rest attached to the lathe ways for supporting long,
slender shafts or other work being turned.
Balance, Running — High-speed pulleys require balancing by running
at speed and seeing that they run without tremor or vibration.
This is called running balance.
Balance, Standing — When a pulley has been balanced on the bal-
ancing ways it is called a standing balance. See Balance-running.
Balancing Ways — Level strips on which the
shaft carrying the pulley or other revolving
body is placed. If the pulley is unbalanced
the heavy side will roll to bottom.
Ball Reamer — See Reamer, Ball.
Bastard — Not regular. The term is usually applied to a file, mean-
ing a cut between the rough and second cut, or to a thread, mean-
ing one that is not of the standard proportions.
Battery. — A combination of chemicals which will give off an electric
current.
Bearings, Ball — Made to reduce friction by interposing balls be-
tween the shaft and the bearing. They are made in various
ways but all aim to have a rolling instead of a sliding action.
Bearings, Roller — Similar to ball bearings except rollers are used
instead of balls. In some cases the rollers are practically hollow
round springs from square stock. These are known as flexible
roller bearings (Hyatt).
Bellows — Devices of wood and leather for
producing a current of air for fanning
fires or blowing dust.
Bearing, Base Plate — For supporting pillow blocks or journal boxes.
Belt Carriers — Pulleys for supporting a long belt between driving
and driven pulleys. May or may not have flanges.
Belt Dressing — Preparation for preserving or cleaning a belt or
making it cling to pulleys.
Belt Fastener — Hooks or other device for joining the ends of belt.
Belt Lacing — Methods of fastening ends of belt with a more or less
flexible joint by means of leather or wire lacing.
Belt, Muley — A belt running around a corner guided by idler pulleys
on a muley shaft.
BOLTS
567
Belt Polisher or Strap — A belt covered with glue and emery or other
abrasive is driven over pulleys and work held against it.
Belt Shifter — Device for shifting belt or belts on countershaft or
elsewhere, from loose to tight pulleys and vice-versa. These are
made in many varieties. Not used where clutches are employed.
Belt Tightener — Loose pulleys arranged for taking up slack of belts;
often called idlers.
Bench — Usual hight is 34 to 35 inches from floor to top of bench,
width about 29 inches. Should be 3 inches from wall to allow
circulation of air, in order to give sprinklers a chance at a fire
underneath.
Bench, Leveling — Bench with a level surface so that work can be
laid on it to test. Made of iron.
Bending Machine — For bending rods, beams, rails, plate, etc. Run
by hydraulic or other power.
Bevel — A tool for measuring or laying off
bevels as shown.' Also a surface not at
right angles to the main surface; may
be any angle. When at 45 degrees
sometimes called a miter.
Blocks, Differential — Hoisting apparatus consisting of differential
gears for lifting heavy loads.
Blocks, Tackle — Sheaves or pulleys mounted in a shell or case, used
with hoisting ropes or chains to raise heavy weights.
____^ Blow Pipe — A pipe for blowing a jet of air
rinto a flame for heating work locally,
such as soldering. The upper picture
is a plain one for use with an alcohol
lamp, the other has a gas and an air
tube. Each is regulated by the small
valve so as to make the hottest flame.
BOLTS
Agricultural Bolt. Agricultural bolts, as indicated by the name, are
B^^^^^^^^^^^ r^ used In farm machines and appliances.
^^^^^^S|||_J The body of the bolt has a series of hel-
^^'^^^^^^^^^^'^^^^'|_J ical lands and grooves which are formed
by a rolling process.
A. L. A. M. Bolt — This bolt is adopted by
the Association of Licensed Automobile
Manufacturers. It has a slotted head
and castellated nut.
568
BOLTS — Continued
Boiler Patch Bolt — A bolt used in fastening
patches on boilers. The patch is coun-
tersunk for the cone head, and boiler
shell tapped for bolt thread. The square
head is knocked off after bolt is screwed
in place.
Coupling Bolt — Bolts for shaft couplings
are finished all over and must be a
close fit in the hole reamed in the two
flanges of the coupling, so that the
sections shall be rigidly secured to-
gether.
Expansion Bolt — In attaching parts to brick, stone or concrete
walls and floors, expansion bolts are frequently employed. The
Star" bolt in the illustration has an
/f
\
1
\ 1
u
.'.i'iwKimdfft
VVVs/vi/ ^\r
u-|^^aJ internally threaded, split sleeve which is
^]^JJ slipped into a hole made in the wall and
then expanded by running in the screw.
The projections on the surface of the shell, and the fact that the
hole receiving it is made larger at the rear, assure the device
holding fast when the expander is in place.
Hanger Bolt — This bolt is used for at-
^^^ taching hangers to woodwork and
IIPW/* consists of a lag screw at one end with
a machine bolt thread and nut at the
other.
Machine Bolts
B
Hexagon Head
0 ^ ■■(]■
Square Head
Round Head Square Countersunk Head
Miscellaneous Bolts
Ci
^ »
Tire
Loom or Carriage
Oval T-Head
Joint
BOLTS — Continued
569
ill
Step
t=^^)>
Deck
Bridge or Roof
Sink
Track
V QtfD
u
Hook
"North" Bolt — The "North" bolt is
used in agricultural machinery and
appliances and has a series of longi-
tudinal lands rolled on the body to
the same diameter as the bolt.
Plow Bolt — Several types of plow and
cultivator bolts are shown in the
accompanying engravings, the forms
illustrated being typical of a variety
of bolts manufactured for agricultural
apparatus.
A — Large Round Head
B — Square Head
C — Round Head, Square Shank
D — Round Head
E — Kev Head
F — Tee Head
G — Button Head
H — Concave Head
I — Reverse Key Head
J — Large Key Head.
570
BOLTS — Continued
Flat or Countersunk
Head
Stove Bolt — Stove bolts are made in
sizes ranging from 5 to | inch. There
is no standard form of thread for
these bolts to which all makers ad-
here, and even the same makers in
some cases have a diiTerent shape of
thread for different sizes of bolts.
The heads commonly formed are the
round, or button head, and the flat
or countersunk head.
Tap Bolt — Tap bolts are usually threaded
the full length of the body, which is not
machined prior to running on the die.
Only the point and the under side of
the head are finished. They are not
hardened and are used as a rule for
the rougher classes of machine work.
The heads are the same width as
machine bolt heads.
Square Head
T-Head Planer Bolt
T-Head Planer Bolt — A bolt with a
T-head having oblique ends which
may be dropped into the T-slot of a
planer and locked by giving it a quar-
ter turn, until the sloping ends strike
against the sides of the slot. Com-
monly employed for holding work on
the planer table.
Bolt Cutter — IMachine for threading bolts, cutting threads on them.
Bolt Header — Machine for upsetting the bolt body to form the
head.
Bolster — A block sometimes called the die block, in which a punch
press die is held. It is attached to the bed by bolts at either end.
Boring and Turning Mill — Machine
having a rotating horizontal table
for the work with one or more sta-
0 0 y^ f^y tionary vertical tools for boring,
turning or facing; a turret is often
Bolster provided for holding a number of
tools in one of the heads. Often
called "vertical mill.** Horizontal boring machines are not called
"mills."
BORING MACHINE
571
fO -"t wivo t^OO 0»
572
BORING MILL
^^^^
-^3
BORING MILL-
- VERTICAL — NILES
I.
Base.
14. Counterweight.
2.
Table.
15. Cross- feed screw.
^^
Housing.
16. Cross-feed screw.
4-
Cross-rail.
17. Vertical feed rod.
=^-
Saddle.
18. Power feed gears.
6.
Swivel.
19 Housing slides.
7-
Right spindle.
20. Vertical cross-rail screw.
8.
Left spindle.
21. Cross-rail hoist.
q-
Tool heads.
22. Vertical power rod.
lO.
Vertical feed wheels.
23. Gear box.
II.
Power feed lock.
24. Power control handle.
12.
Spindle bearings.
25. Driving pulleys,
13.
Counterweight chain.
86, Chuck jaws.
BOX CHUCK— BUTT WELD 573
Box Chuck — A two-jawed chuck of rectangular form used by brass
finishers.
Brass — Alloy of copper and zinc although a little tin is often added
for strength and density. Common proportion is copper 66,
zinc 34. See bronzes, also low and high brass.
Brass, High — ■ Only applied to rolled material. Two parts copper,
one of zinc. Color is light yellow.
Brass, Low — Only applied to rolled material. Ranges from 75 per
cent, copper to 25 of zinc to 88 per cent, copper and 12 of zinc.
Brazing — The joining of metals by the use of copper filings or
chips and borax or some other flux. This is usually called
spelter or hard solder and can be applied to almost any of the
harder metals.
Brazing Clamps — Clamps to hold the ends of band saw or other
work for brazing.
Broach — A tool which is practically a series of chisels or cutting
edges for enlarging holes or changing their shape. Generally
used for odd shaped holes but occasionally for rounds. The
teeth should be on an angle to give a shearing cut. Name
is sometimes given to a small reamer used by jewelers.
Bronzes — Alloy of Copper and Tin. Used in coinage, in bells,
statuary, musical instruments and mirrors. Bell metal is 80
copper, 20 tin to 84 copper, 16 tin.
Bulldozer — Heavy forming machine for bending iron or steel and in
which the dies move horizontally. Very similar to a forging
press.
Bull Blocks — Blocks through which wire or rods are drawn to reduce
size.
Bull "Wheel — Usually applied to the gear of a planer which meshes
into the rack under the table and drives it.
Bunsen Burner — A device for securing
a very hot flame by mixing air and
©h" il^^^^^^ g3.s in a chamber behind the flame.
The one shown has two pieces which
make the flame flat' instead of round.
Burnishers — Tools of hardened and polished steel for finishing brass
and softer metals by friction. They are held against the revolving
work and give a smooth surface by compressing the outer layer
of the metal.
Burring Machine — For removing burrs from hot pressed nuts.-
Bushing — Tube or shell which reduces the diameter of a hole.
Hardened bushings are used in jig work to guide drills or other
tools.
Butt Joint — A riveted joint with the ends of the plates abutting
squarely against each other.
Butt Weld — A weld in which the ends of the two pieces simply abut
against each other for welding together.
574
CALIPERS
Button — A steel bushing, hardened and ground, used for locating a
jig plate or some similar piece in which holes have to be bored
in exact position. The
button is attached to
the work by a small
screw and is then ad-
justed by a micrometer
or othenvise until it is
central at the exact
point where it is desired
to bore the hole. The
work is then placed on
the face plate of the
lathe, and with a test in-
dicator resting on the outside of the button, the piece is readily set
central. It is then clamped fast to the face plate, the button is re-
moved and the hole bored. Frequently, several buttons are used on
the same piece of work, their relative positions being adjusted to
conform to the center distances required between holes. The work
is then indicated true by each button in succession, and one hole
after another bored.
CALIPERS
Finn Joint Calipers — Having a large, firm
joint in place of old style plain riveted
joint. This is an inside caliper.
Gear Tooth Caliper — A caliper with two
beams at right angles. The vertical
beam gives tooth depth to pitch line
and the other the thickness at pitch
line. Both have verniers. Used in
measuring teeth for accuracy.
Hermaphrodite Caliper — A combination of
one leg of a divider and one feg of a
caliper. Used in testing centered work
and in laying off distances from the edge
of a piece.
Keyhole Caliper — Has one straight leg and
the other curved.
Micrometer Caliper — A measuring in-
strument consisting of a screw and
having its barrel divided into small
parts so as to measure slight degree?
of rotation. Usually measure to thou-
sandths, sometimes to ten-thousandths
CALIPERS — Continued
575
Transfer Caliper.
Odd Leg Caliper — Calipers having both
legs pointing in the same direction.
Used in measuring shoulder distances
on flat work, boring half round, boxes
etc.
Outside, Spring Caliper — Tool for measuring
the outside diameter of work. Controlled
by spring and threaded nut. JNuts are
sometimes split or otherwise designed to
allow rapid movement when desired, final
adjustment being made by screw.
Slide Caliper — A beam caliper made with
a graduated slide. Generally made
small for carrying in the pocket.
Square-micrometer Caliper — A beam cali-
per having jaws square with the blade,
and having a micrometer adjustment to
read to thousandths of an inch.
Thread Caliper — Similar to outside calipers
except it has broad points to go over the
tops of several threads.
Caliper which can be set to a given size, the-
auxiliary arm set, and the calipers opened
at will, as they can be reset to the aux-
iliary arm at any time. Used to caliper
recesses and places where they must be
moved to get them out.
Cam, Drum or Barrel — The drum cam
has a path for the roll cut around the
periphery, and imparts a to-and-for
motion to a slide or lever in a plane
parallel to the axis of the cam. Some-
times these cams are built up of a
plain drum with cam plates attached.
Cam, Edge — Edge or peripheral cams (also
called disk cams) operate a mechanism
in one direction only, gravity, or a
spring, being relied upon to hold the
cam roll in contact with the edge of
the cam. On the cam shown, a io h '^
the drop; h \.o c the dwell; c to d, rise; i
to a, dwell.
576
CAM — CENTER PUNCH
Cam, Face — Face cams have a groove
or roll path cut in the face and oper-
ate a lever or other mechanism posi-
tively in both directions, as the roll is
always guided by the sides of the slot,
m
"C" Clamp — See Clamp "C."
"C" Washer.— See Washer, Open.
Carbonizing — The heat treatment of steel so that the outer surface
will be hard. The surface absorbs carbon from the material
used.
Card Patterns — Patterns made on a gate so as to be all molded at
once and to provide gates for the metal to flow.
Case-hardening — A surface hardening by which the outer skin of a
piece of iron or steel absorbs carbon or carbonizes so as to harden
when cooled in water. The piece is usually packed in an iron
box with bone, leather or charcoal, or all three, and heated slowly
several hours, then quenched.
Cat Head — A collar or sleeve which fits loosely over a shaft and is
clamped to it by set screws. Used for steady rest to run on
where it is not desired to run it on the work.
Same name is also given to the head carrying cutters on boring
bars.
Cat Head Chuck — A chuck in which the end of a shaft or other
piece is driven by a number of set screws tapped through the wall
of the chuck.
Cathode — The negative terminal of an electric bath or battery.
Center, Dead — The back center or the stationary center on whic
the work revolves. On many grinding machines both cente;
are dead.
Center, Live — The center in the revolving spindle of a lathe or
similar machine. It is highly important that this should run
true or it will cause the work to move in an eccentric path.
Center Punch — Punch for marking points
p^ '^^^sm^ °" metal. Made of steel with a sharp
^ ^^^m -— > point and hardened. Often called a
prick punch.
Center Punch, Automatic — Has a spring actuated hammer in the
handle, which is released when the handle is pressed way down.
The point can be placed where desired
f-^ — Tt— □=. ^"^ the blow given by a pressure of
\ ^^^^^ III — '-' the hand. In some cases the blow can
be varied.
k
CENTER PUNCH — CHUCK
577
Center Punch, Bell or Self-centering — A
center punch sliding in a bell or cone
mouthed casing so when placed square
over the end of any bar it will locate
the center with sufficient accuracy for
most purposes.
Center Punch, Locating — Having an extra leg which has a spring
point and is adjustable. The spring point is placed in the first
Q punch mark and so locates the next
(I ■ (-° ^ '. — -, punch mark at the right distance from
' ^ the first.
Centering Machines — For drilling and reaming center of work for
the lathe or grinder.
Chamber — A long recess. See Recess.
Chasers — Tools used for cutting threads by chasing. Usually have
several teeth of right pitch, but name is sometimes applied to a
single point tool used in brass work on a Fox lathe. Chasers
are made circular or flat and in the old days many were used by
hand.
Chasing Threads — Cutting threads by moving a tool along the work
at the right speed to give the proper pitch. Distinguishes between
threads cut with a die and those cut with a threading tool.
Chattering — A slight jumping of the tool away from the work or
vice-versa, and which leaves little ridges in same direction as the
teeth. Occurs at times in any class of work and with any kind
of tool. Due to springing of some parts of the machine.
Cherry — See Cutters, Milling.
Chisel, Blacksmith's Hot — A chisel for
cutting hot metal. Has a handle so
that it can be used without getting the
hand too near the heated metal.
Chipping — The cutting of metal with cold chisel and hammer.
Also used when a piece "chips" or breaks out of a piece or punch.
Chisel, Cape — Chisel with a narrow blade for cutting keyways and
similar work.
Flat Cold Chisel
Diamond
Cape
Chisel, Cold — The usual machinists*
chisel for cutting or "chipping"
metal with a plain cutting edge as in
illustration.
Chisel, Diamond or Lozenge — Similar
to a cape chisel but with square end
and cutting edge at one corner. Used
for cutting a sharp-bottomed groove.
Round
Chisel, Round — A round end chisel with the cutting edge ground
back at an angle. Used for cutting oil grooves and similar work.
Chuck, Draw — Operated by moving longitudinally in a taper bear*
ing. Used on precision work.
57^
CHUCK — CIRCUIT
Chuck, Drill — A chuck made especially for holding drills in drilling
machines. Sizes run from the smallest up to one inch.
Chuck, Eccentric — For turning eccentrics or other work in which
hole is not concentric with outside. Usually made adjustable to
suit varying degrees of eccentricity.
Chuck, Expanding — For turning hollow work which must be held
on inside. Jaws go inside of work.
Chucks, Lathe — Devices for holding work.
Usually screw on spindle and have two,
three or four jaws. These may be inde-
pendent or move together by screws
only (in case of two jawed) or screws
and gears in case of more than two.
There is also a spiral or scroll chuck
without gears or screws of the ordinary
kind.
Chuck, Magnetic — Has no jaws but holds iron and steel by magnet-
ism.
Chuck, Master — The main body of a screw chuck which screws on
the nose of the lathe spindle and which carries the sub- or screw-
chuck for holding the work. Mostly used in brass work.
Chuck, Nipple — For holding short piece of pipe to be threaded.
Chuck, Oval — Chuck designed to move the work to and from the
tool so as to produce an oval instead of a round. Sometimes
called an elliptic chuck.
Chuck, Planer — For holding work on
bed or platen of planer, shaper or
milling machine. Sometimes called a
vise. They are made with both plain
and swivel bases as shown, and usually
have locking strips which hold the
piece carrying the set screws.
Swivel Base
Chuck, Screw — Chucks made with internal or external thread to
hold work which has been already threaded. These very often
screw into a master chuck. Mostly used in brass work.
Chuck, Spring — See Screw Machine Tools.
Chucking Machines — Usually have a turret for tools, a revolving
chuck or table for work, and generally used for boring and ream-
ing. May be either vertical or horizontal.
Circuit — The path in which an electric current flows.
CLAMP — COMPOUND REST
579
Clamp, "C" — Clamp shaped like a letter
"C" for holding work in various ways.
Are sometimes cast but more often drop
forged for heavier work.
Clamps, Machinist — Clamps for holding
work together, holding jigs or templets
on work, etc.
Clash Gears — Gears which are throvm into mesh by moving the
centers together and sometimes by sliding the gears on parallel
shafts till the teeth get a full bearing. The latter are some-
times called sliding gears.
Clutch — ■ Any device which permits one shaft to engage and drive
another, may be either friction or positive, usually the former.
Made of all sorts of combinations of cams, levers and toggles.
Clutch, Friction — A device whereby motion of loose pulley is trans-
mitted to shaft to be driven. Various methods are employed but
all depend on forcing some kind of friction surfaces together so
that one drives the other.
Clutches, Positive — Devices for connecting
machines to a constantly running shaft
or one part to another, at will. There
are many kinds, both positive and fric-
tion. The illustrations show two of the
most common of the positive clutches.
Square Jaw Clutch
Collar — A ring used for holding shafting, loose pulleys, in proper
position or for fastening to boring tools to prevent them going in
too deep.
Collar, Safety — Having a clamping device instead of set screw or
having set screw below surface or so covered as not to catch
anything brought in contact wath it.
Commutator — The part of a dynamo or motor which takes off or
leads current into the machine.
Compound Rest — An auxiliary tool slide on lathe carriage arranged
to swivel so as to turn at any desired angle with the lathe centers
or with cross slide. Usually graduated into degrees.
58o
COTTER — COPING MACHINE
Cotter, Spring — Also called split cotter, split pin, etc., is used in a
hole drilled crosswise of a stud, shaft
/" X _^ or some similar member, and its ends
( 0>- ^ spread apart to retain it in place and
v^^y ^ keep some member carried by the
shaft from slipping off.
Counterbore — Has a pilot to fit a hole already drilled, or drilled
and reamed, and its body with cutting
edges on the end is used to enlarge the
hole to receive a screw head or body or
for some similar purpose.
Countershaft — The shaft for driving a machine which is itself driven
by the main or line shaft.
Coupling, Clamp — Couplings made in
two or more parts, clamping around
the shafts by transverse bolts. Hold
either by friction or have dowels in
shaft. Sometimes called compression
although this is confusing.
Coupling, Compression — Grips shafting by
drawing together tapered parts. This
forces them against shaft and holds it
firmly. Bolts parallel with shaft draw
parts together.
Coupling, Flanged — A flange is keyed to each
shaft and these flanges are bolted together.
Also called "plate" coupling.
Coupling, Friction — Couplings which depend on frictional contact
Coupling, Jaw or Clutch — Positively engaged by jaws or projections
on the face of opposing parts.
Coupling, Shaft — Devices for fastening ends of shafting together so
that both may be driven as one shaft. These are made in a
great variety of ways, from plain set screw coupling to elaborate
compression devices.
Coupling, "Wedge — Coupling that clamps the shaft with a wedging
action. Practically like a compression coupling. Generally en-
closed in a sleeve. Also called vise coupling.
Cope — The upper part of a flask.
Coping Machine — For cutting away the flanges and comers of beams
and bending the ends.
COUNTER — CUTTERS, MILLING 581
Counter, Revolution — Device for counting
the revolutions of a shaft. Generally
made with a worm and a gear having
100 teeth so that one turn of dial equals
100 revolutions.
Countershaft — Shaft carrying tight and loose pulleys (or friction
clutch pulleys) for starting and stopping machines or reversing
their motion.
Crane, Gantry — Traveling crane mounted on posts or legs for yard
use.
Crane, Jib — Crane with a swinging boom or arm.
Crane, Locomotive — Crane mounted on a car with an engine so as
to be self-propelling on a track.
Crane, Pillar — Having the boom or moving arm fastened to pillar
or post.
Crane, Portable — Hoisting frame on wheels which can be run around
to the work and used to handle work in and out of lathes and
other machines.
Crane, Post — See Crane, Pillar.
Crane, Swing — Same as Jib Crane.
Crane, Traveling — Crane with a bridge or cross beam having wheels
at each end so it can be run on overhead tracks to any point in
the shop.
Crimping — Fluting, corrugating or compressing metal ring to re-
duce its diameter.
Cross-rail — The part of a planer, boring mill or similar machine on
which the tool heads or slides move and are supported.
Cut Meter — Instrument for measuring the
surface speed of work either in lathe or
planer. A wheel is pressed against the
moving surface and the speed is shown
in feet per minute.
Cutters, Flue Sheet — Special cutters for making holes as for flues,
in flue sheets or in other sheet metal or structural work.
CUTTERS, MILLING
Angular Cutters — Such cutters are used
for milling straight and spiral mills,
ratchet teeth, etc. Cutters for spiral
mill grooving are commonly made
with an angle of 12 degrees on one
side and 40, 48 or 53 degree angle on
the other.
^82 CUTTERS, MILLING — Continued
Cherry — A form of milling cutter which is more strictly a formed
reamer, for finishing out the interior
of a die or some similar tool. The
cherry shown is for a bullet mold.
Convex and Concave Cutters — Convex
and concave cutters are used for mil-
ling half circles. The convex cutter
is often used for fluting taps and
other tools. Like all other formed
cutters the shape is not affected by
the process of sharpening.
Comer Rounding Cutters — Left hand
double and right hand cutters of this
type are used for finishing rounded
corners and edges of work. The
shape of the cutter is not altered by
grinding on the face of the teeth.
Cotter Mill — This type of mill is used
for cutting keyseats and other slots
and grooves.
Dovetail Cutters — Male and female dove-
tails are milled with these tools, and
edges of work conveniently beveled.
Left Haud
£ight Haud
^
:3
Left Hand Mill
Left Hand
Bight Hand
End Mill — This mill sometimes called
a butt mill, is used for machining
slots, milling edges of work, cutting
cams, etc.
End Mill (with center cut). This end
mill has clearance on the inner side
of the end teeth and is adapted to
cut into the work to a depth equal
to the length of the end teeth and
then feed along, dispensing with the
necessity of first drilling a hole, which
has to be done when the inner sides
of the teeth are not relieved.
The mills are Often used for heavy cuts particularly in cast iron.
COTTERS, MILLING — Continued
5S3
Face
Pormed
7
Arbor
Face and Formed Cutters — The face cutter
to the left, of Brown & Sharpe inserted
tooth type is made in large sizes and
cuts on the periphery and ends of teeth.
The formed cutter to the right may
be sharpened by grinding on the face
without changing the shape. For mill-
ing wide forms several cutters are often
placed side by side in a gang.
Fish Tail Cutter — A simple cutter for
milling a seat or groove in a shaft or
other piece. Usually operated at
rapid speed and light cut and feed.
Fluting Cutters — Cutter A is an angular
mill for cutting the teeth in spiral
mills, cutter B is for tap fluting and
C for milling reamer flutes. In each
case the cutter is shown with one
face set radial to the center of the
work.
Fly Cutters — Fly cutters are simple formed
cutters which may be held in an arbor like
that shown at the top of the group. The
arbor is placed in the miller spindle and
the tool or other work to be formed is
given a slow feed past the revolving cutter.
After roughing out, the cutter can be held
stationary and used like a planer tool for
finishing the work which is fed past it
and so given a scraping cut.
1
Gang Cutters — Cutters are used in a gang
on an arbor for milling a broad sur-
face of any desired form. The cutters
shown have interlocking and overlap-
ping teeth so that proper spacing may
be maintained. In extensive manufac-
turing operation the gangs of cutters
are usually kept set up on their arbor
and never removed except for grinding.
584
CUTTERS, MILLING — Continued
Gear Cutter (Involute). In the Brown
& Sharpe system of involute g;ear
cutters, eight cutters are regularly
made for each pitch, as follows:
No. I will cut wheels from 135 teeth
to a rack.
No. 2 will cut w'heels from 55 teetli
to 134 teeth.
No. 3 will cut wheels from 35 teeth
to 54 teeth.
No. 4 will cut wheels from 26 teeth
to 34 teeth.
No. 5 will cut wheels from 21 teeth
to 25 teeth.
No. 6 will cut wheels from 17 teeth to 20 teeth.
No. 7 will cut wheels from. 14 te^th to 16 teeth.
No. 8 will cut wheels from 12 teeth to 13 teeth.
Such cutters are always accurately formed and can be sharp-
ened without affecting the shape of the teeth.
Gear Cutters, Duplex — The Gould & Eberhart
duplex cutters are used in gangs of two 01
more; the number of cutters in the gang
depending on the number of teeth in the
gear to be cut. The following table gives
the number of cutters which may be used in
cutting different numbers of teeth.
Under 30 teeth i cutter
Over 30 teeth 2 cutters
50 teeth 3 cutters
70 teeth 4 cutters
95 teeth 5 cutters
120 teeth 6 cutters
150 teeth 7 cutters
I So teeth 8 cutters
Over
Over
Over
Over
Over
Over
Over
Over
230 teeth 10 cutters
260 teeth 12 cutters.
Gear Stocking Cutter — The object
stocking cutters is to rough out the
teeth in gears, leaving a smaller
amount of metal to be removed by
the finishing cutter. They increase
the accuracy with which gears may be
cut, and save the finishing cutter as
well.
In all cases where accuracy and smooth
running are necessary the gears should
first be roughed out. One stocking
cutter answers for all gears of the
same pitck.
CUTTERS, MILLING — Conlmual
585
Hob — A form of milling cutter with
teeth spirally arranged like a thread
on a screw and with flutes to give
cutting edges as indicated. Used for
cutting the teeth of worm gears to
suit the worm which is to operate the
gear. Hobs are formed and backed
off so that the faces of the teeth
may be ground without changing the
shape.
Inserted Tooth Cutter — Brown & Sharpe inserted tooth cutters have
taper bushings and screws for holding
the blades in position in the bodies.
Inserted tooth construction is generally
recommended for cutters 6 inches or
larger in diameter. There are many
types of inserted tooth cutters and in
most cases the blades are readily re-
moved and replaced when broken or
worn out.
Inserted Tooth Cutter (Pratt & Whitney). In
this type of cutter the teeth or blades are
secured in position by taper pins driven into
holes between every other pair of blades; the
cutter head being slotted as shown to allow
the metal at each side of the taper pin to be
pressed firmly against the inserted blades.
Interlocking Side Cutters — These cutters
have overlapping teeth and may be
adjusted apart to maintain a definite
width for milling slots, etc., by using
packing between the inner faces.
Plain Cutters — These cutters are for
milling flat surfaces. When over |
inch wide the teeth are usually cut
spirally at an angle of from 10 to
15 degrees, to give an easy shearing
cut. When of considerable length
relative to diameter they are called
slabbing mills.
586
CUTTERS. MILLING — Continued
Rose Cutter — The hemispherical cutter
known as a rose mill is one of a large
variety of forms employed for working
out dies and other parts in the- profiler.
Cutters of this form are also used for
making spherical seats for ball joints, etc.
Screw Slotting Cutter — Screw slotting cutters
have fine pitch teeth especially adapted
for the slotting of screw heads and similar
work. The cutters are not ground on the
sides. They are made of various thick-
nesses corresponding to the numbers of the
American Wire Gage.
Shank Cutter — Shank milling cutters are
made in all sorts of forms with shanks
which can be conveniently held true in
miller or profiler while in operation.
Shell End Cutter — Shell end mills are de-
signed to do heavier work than that for
which the regular type of end mills are
suited. They are made to be used on an
arbor and are secured by a screw in the
end of the arbor. The end of the cutter
is counterbored to receive the head of the
screw and the back end is slotted for
driving as indicated.
Side or Straddle, and Slabbing Cutters —
Side cutters like that to the left cut on
the periphery and sides, are suitable
for milling slots and when used in
pairs are called straddle mills. May be
packed out to mill any desired width
Slabbing of slot or opposite faces of a piece of
any thickness.
Slabbing cutters are frequently made with nicked teeth to
break up the chip and so give an easier cut than would be possible
with a plain tooth.
Slitting Saw, Metal — Metal slitting saws are
thin milling cutters. The sides are finished
true by grinding, and a little thicker at the
outside edge than near the center, for proper
clearance. Coarse teeth are best adapted
for brass work and deep slots and fine teeth
for cutting thin metal.
Side
CUTTERS, MILLING — Continued
587
Sprocket Wheel Cutter — Cutters for milling the
teeth on sprocket wheels for chains are formed
to the necessary outHne and admit of grinding
on the face Hke regular gear cutters, without
changing the form of the tooth.
Straight Shank Cutter — Straight shank
cutters of small size are extensively used
in profilers and vertical millers for die
sinking, profiling, routing, etc. They
are held in spring chucks or collets.
T-Slot Cutter — Slots for bolts in miller
and other tables are milled with
T-slot cutters. They are made to
standard dimensions to suit bolts of
various sizes. The narrow part of
the slot is first milled in the casting,
then the bottom portion is widened
cut with the T-slot cutter.
Woodruff Key Cutter — The Whitney Mfg.
Go's keys are semi-circular in form and
for cutting the seats in the shaft to
receive them a cutter of the type shown
is used. These cutters are made of
right diameter and thickness to suit
all the different sizes of keys in the
Woodruff system.
Cutting-off Machine — For cutting desired lengths from commercial
bars of iron, steel or other material, usually has stationary tools
and revolves the work. The latter is gripped by the rotating
chuck; and as the tools are fed toward the center, the spindle in
some types of machines is driven at an accelerated speed so that
as the diameter of the cut is reduced, the speed of rotation is in-
creased to maintain a practically uniform surface speed of work.
In cold-saw cutting-off machines, the work is held in a vise and a
rotating circular cutter is fed against it. Such machines are used
not only for severing round stock but also for cutting off square
and rectangular bars, rails, I-beams, channels and other struc-
tural steel shapes.
Cutting-off Tool Post — The tool block used on the cross slide of a
turret lathe or other machine for carrying the tool for cutting off
the completed piece of work from the bar of material held in the
chuck. The tocl post may be made to receive a straight tool or
a circular cutter.
588
DIES, PUNCH PRESS
Daniels Planer — See Planer.
Dead Center — The center in the tail spindle of a lathe or grinder
which does not revolve.
Derrick — Structure consisting of a fixed upright and an arm hinged
at bottom, which is raised and lowered and usually swings around
to handle heavy loads.
Dial Feed — A revolving disk which carries blanks between the
punch and die.
Diamond Hand Tool — Used for dressing grinding wheels after they
have been roughed out with the cheaper
l_j-||T| — -ir^ forms of cutters. Fixed diamonds are
"^ ^-Ul — -JL^ usually considered better than those
held by hand.
Die Chasers — Threaded sections inserted in a die head for cutting
bolts and screws. ,
Die, .Screw Plate or Stock — A frame or
handle for holding a threading die. Some-
times die and handles are of one piece.
Die, Spring or Prong — Die with cutting
portions in the end of prongs; can
be adjusted somewhat by springing
prongs together with a collar on
outside.
Dies, Bolt — Dies for cutting bolts. Some are solid, others adjustable.
Some for hand die stocks or plates but mostly for machine bolt
cutters.
DIES, PUNCH PRESS
Bending Dies, Compound-
In compound bending dies of the type
shown the work is car-
ried down into the die
by punch A, and held
there while the beveled-
fingers B act upon the
slides C and cause them
to move forward in the
top of die D and bend
the material to the out-
line of the punch. Upon
.the up-stroke of the
punch the slides C are
pressed outwardly by
their springs and. the
bent piece of work is removed by the punch from the die. It will
be seen that the holder for punch A^ upon which depends the in-
terior form of the piece being bent, is not positively secured in its
holder, but is instead adapted to slide up and down in its sea^
DIES, PUNCH PRESS — Continued
589
although prevented from turning by a small pin at the upper end
of the shank which is engaged by a slot in the punch carrier. The
springs shown above the punch proper tend to hold the punch in
its lower position and at the same time after the punch has passed
down into the die allow the punch carrier to descend still further
to press fingers B into operation against slides C which bend the
work to the outline of the punch.
Bending Dies, Plain — Simple bending
dies are made with the upper face of
the die and the bottom of the punch
shaped to conform to the bend it is
desired to give the blank. A common
type is shown in the engraving.
In simple bending dies the upper face of the die is cut out to
the desired form and the piece of work formed to required shape
by being pressed directly down into the die by the punch.
Blanking Dies — Blanking dies are about
the most commonly used of all the
varieties of press tools. A simple form
of die is seen in the illustration. The
strip of sheet metal is fed under the
stripper and is prevented by that mem-
ber from lifting with the punch upon
the up-stroke, following the punching
out of the blank. \Vhere several
punches are combined in one hole for
blanking as many pieces simultane-
ously, they are known as multiple
blanking tools.
Bulging Dies — The "before and after"
sketches show the character of the
work handled in bulging dies. The
shell after being drawn up straight
is placed over mushroom plunger A
in the bulging die, and when the
punch descends the rubber disk B is
forced out, expanding the shell into
the curved chamber formed by the
punch and die. Upon the punch
ascending, the rubber returns to its
original form and the expanded work
is then removed.
o
i nil
.^0. °.s>_.
VO 1
Die
Burnishing Dies — Burnishing dies are made a little smaller at the
bottom than at the top and when the work is forced ^ovm through
the die, the edge of the piece is given a very high finish making
590
DIES, PUNCH PRESS — Continued
polishing and hand finishing operations unnecessary. The bur-
nishing process forms a very accurate sizing method also.
Coining Dies — Coining dies are operated in veiy powerful presses
of the embossing type
similar to those used
for forming designs
on silverware, medals,
jewelry, etc. The po-
sition of the work,
the retaining coller
and the dies are indi-
cated aX A, B, and C.
In the latter section the coin is shown delivered at the top of the
die.
Combination Dies — Combination dies are used in single acting
presses for such work as cutting a blank and at the same stroke
turning down the edge
and drawing the piece
into the required
shape. In most cases
the work is pushed out
of the dies by the ac-
tion of a spring. Such
a set of dies is shown
in the engraving, for
making a box cover
and body. The work
is blanked by cutting-
punch -4, and formed
to the right shape by
B and C, the former
holding the piece by
spring pressure to the
block C while punch A ,
continuing to descend,
draws the box to the required shape. Ring D acts as an
ejector or shedder and is pressed down, compressing the rubber
at E during the drawing operation, and upon the up-stroke of the
punch, ascends and ejects the work from the dies.
Dies of this type, with a spring actuated punch or die inside the
regular blanking tool, are often used for simultaneously blanking
and piercing, blanking and bending, etc.
It will be noticed that the lower view in the group show'ing the
work at the right-hand side of the sectional illustration of the die,
represents the box cover and body as they appear when assembled
after' the superfluous metal in the flange or "fin" has been re-
moved in a trimming die. This fin as left on the piece when com-
ing from the combination die is shown in the view immediately
under the blank. A trimming die for finishing such work evenly
is shown on page 597.
DIES, PUNCH PRESS — Continued
591
Compound Dies — Co m-
pound dies have a die
in the upper punch
and a punch in the
lower die. The ferrule-
making tools shown have
a blanking and outer
drawing punch A, with
a central die B, to re-
ceive lower punch C
which cuts out the cen-
ter of the ferrule blank
and allows the metal to
be drawn down inside
as well as outside of the
bevel edged member D.
As the work is drawn
down ring E descends
com})ressing rubber cush-
ion F below and upon
the return movement the
ferrule is ejected from the
die.
Cupping Dies — Used for drawing up a cup from a disk or planchet.
Same as drawing dies.
Curling Dies — Curling dies are used for producing a curled edge
around the top of a piece drawn up
from sheet metal. When the top is to
be stiffened by a wire ring around
which the metal is curled, a wiring die
is used, the construction of which is
practically the same as the curling die.
The illustration shows a curling die
and the appearance of a shell at
various stages during the operation
of curling over the edge. The dia-
grams A, B, C, D, show the progress
in the curling process as the punch
descends, pressing down on the edge
of the straight drawn shell.
Dinking dies, or hollow cutters, although not usu-
ally classed with regular dies are used
so commonly as to entitle them to be
listed in that class. They are adapted
to punching out all sorts of shapes
from leather, cloth, or paper. The
edges of the dies (a few specimens of
which are shown in the engraving) are
usually beveled about 20 degrees out-
side. Where made for press use the
handle is omitted. As a surface for
Dinking Dies
592
DIES, PUNCH PRESS — Continued
the cutting edge of the die to strike on, a block is built up of
seasoned rock maple, set endwise of the grain.
Double Action Dies — This type of die is used in a press which has
a double acting ram; that is, there are two slides, one inside the
other, which have different strokes.
To the outer slide is fastened the com-
bined cutting punch and blank holder
A, which is operated slightly in ad-
vance of the drawing punch B actu-
ated by the inner slide. The blank
upon being cut from the stock by A,
drops into the top of the die at C and
is kept under pressure by the flat end
of cutting punch A to prevent its
wrinkling, while punch B continues
downward drawing the metal from
between the pressure surfaces and into the shape required.
Drawing Dies, Plain — Dies of the type
shown can be used for shallow draw-
ing only, as there is no pressure on
the blank to prevent its wrinkling
when forced down into the die by
the punch. The blank fits the recess
A in the upper face of the die and
the die itself which is slightly tapering
is made the diameter of the punch
plus twice the thickness of the wall
required for the shell. The bottom
edge B of the die strips the shell from
the punch when the latter ascends.
Re-drawing dies are used for drawing
out a shell or cup already formed
from the sheet metal. In the illus-
tration, a shell ready for re-drawing
is shown in position in the dies, which
need little explanation. The work is
located in the upper plate /I, and after
being forced through the die B, is
stripped from the punch by edge C.
Ordinarily, a shell which is to be
given considerable elongation, is passed through a number of re-
drawing dies.
Re-drawing dies are sometimes referred to as reducing dies^
although the latter, as explained under the proper heading on
page 5q4, are used for drawing down the end of a shell only, as
in the case of a cartridge shell, which is made with a neck some-
what smaller in diameter than the body.
DIES, PUNCH PRESS — Continued
593
Fluid Dies — Water or fluid dies are used
for forming artistic hollow ware of
silver, and other soft metals, in exact
reproduction of chased work. The
die as shown is a hinged mold cast
from carved models and finished with
all details clean and sharp. The
shell to be worked is filled with
liquid and enclosed in the die and
a plunger in the press ram then de-
scends and causes the fluid to force
the metal out into the design in the die.
Follow Dies — Follow tools consist of two or more punches and
dies in one punch holder and die body, these being arranged in
tandem fashion so that after the first
operation the stock is fed to the next
point and a second operation per-
formed; and so on. In the die shown,
which is for making piece A, the strip
of metal is first entered beneath stripper.
B far enough to allow the first shell
to be drawn at the first stroke by
punch C and die D. The metal is
then moved along one space and the
shell drawn at the first stroke is cen-
tered and located within the locating
portion of piercing die E. At the
next stroke the hole in the center is pierced with punch F, and
a second shell drawn in the stock by punch and die C and D,
The stock is then fed forward another space and the blanking
punch G cuts out the piece from the metal. At the same stroke
a third piece is being formed on the end of the stock and a sec-
ond hole pierced. Thus three operations are carried on
simultaneously.
Gang Dies — Gang tools have two or more punches and dies in one
I a2^^
holder for making as many openings
in a blank at one stroke of the press.
Sometimes dies which perform a num-
ber of operations on a piece which is
fed along successively under one punch
after another are called "gang" dies;
strictly speaking, however, such tools
are " follow" dies. Where a large num-
ber of punches are combined they are
called a multiple punch, or if they are
of quite small diameter for piercing are sometimes known as
perforating punches.
594
DIES, PUNCH PRESS — Continued
Heading Dies — Heading dies strike up the heads on cartridges and
other shells, and are generally operated in a horizontal heading
machine.
Index Dies — For certain classes of work such as notching the edges
of large disks or armature punchings, an index die is sometimes
used consisting of a rotary index plate adapted to carry the work
step by step past the punches which cut out one notch or a series
of notches at each stroke of the press.
Perforating Dies — Perforating tools consist of a number of piercing
tools in one set of dies
and may be called also
multiple piercing tools.
In the example shown,
which punches a large
number of holes in a
disk, the work is held
by the spring-controlled
pressure-pad A against
the face of the die B
while the punches at
C are forced down
through the sheet metal.
In this case the punches
are easily replaced when
broken, by unscrewing
the holder from the shank and slipping the small punch out from
the back.
Piercing Dies — Piercing tools are used for punching small holes
through sheet metal. Where arranged for punching a large
number of holes simultaneously they are often called perforating
dies.
Piercing Dies, Compound — Compound piercing tools have, in addi-
tion to the regular punches carried by the holder in the ram, a
set of horizontal punches for making holes through the sides of
the work. These side punches are operated by slides moved
inward by wedge-shaped fingers, the arrangement being the
same as in the case of the compound bending dies, an illustration
of which is given under that head.
Reducing Dies — Reducing dies are re-drawing dies for reducing a
portion of the shell only, whereas the regular re-drawing die
reduces the whole length. Reducing dies for cartridge shells
form the familiar "bottle neck" shell now so commonly manu-
factured, with a larg body for the powder and a smaller neck into
which the bullet is secured. In dial feed presses ordinarly em-
ployed for cartridge making operations, two or more reducing
dies are often used for shaping the neck of the shell to the re-
quired dimensions, each die operating in turn upon the shell as it
is carried around step by step under the press tools by the inter-
mittent rotary movement of the feeding dial.
DIES, PUNCH PRESS — Continued
595
Riveting Dies — Riveting dies for the
punch press are provided with cavi-
ties in the working faces to suit the
shape of the head it is desired to pro-
duce on the ends of the rivets.
Sectional Dies — Frequently dies of com-
ph'cated outline are built up in sec-
tions to enable them to be more easily
constructed and kept in order. This
form is resorted to often in the case
of large dies where a break at one
point would mean considerable ex-
pense for a new die. Also the diffi-
culties of hardening are reduced with
the sectional construction. As shown,
the various parts are secured to a
common base or holder.
Shearing Dies — Shearing dies are used
for cutting-off operations, and are fre-
quently combined with other press
tools so that after certain operation son
a piece it can be severed from the end
of the stock. The shearing tools in
the engraving are arranged for simply
cutting up stock into pieces of the
required length and the punch itself
is of the inserted type secured by
pins in its holder.
Split Dies — Split dies form one type of sectional die — the simplest;
they are made in halves to facilitate working out to shape, hard-
Sub-press Dies — A sub-press and its tools are represented on the
following page. Such tools are used for small parts which have
to be made accurately and are very common in watch and type-
writer shops and similar places. The tools are held positively in
line in this press and as a result their efficiency is maintained
indefinitely. The press is slipped bodily into the regular power
press with the base clamped to the press bed and the neck of the
sub-press plunger connected with the ram of the press.
DIES, PUNCH PRESS — Continued
597
Swaging Dies — Swaging operations are resorted to where it is de-
sired to shape up or round over the edges of work aheady blanked
out. Thus in watch wheel work the arms and inside edges of
the rims are sometimes swaged to a nicely rounded form subse-
quently to the blanking out of the whi;cl in the sub-press. Swag-
ing dies for such work are of course made with shallow impressions
which correspond to a split mold between the two halves of which
the blank is properly shaped.
Bullet swaging dies receive the slug as it comes from the bullet
mold and shape the end to the required cone point.
Trimming Dies — Trimming dies remove
the superfluous metal left around the
□ I ^ J edges or ends of various classes of
-^j-^ — drawn and formed work. In the case
T-i *"'* shown, the box body A has been
drawn up and a fin left all the way
round; this is dropped into the trimming
die B and the punch C in carrying it
through the die trims the edge oflf evenly,
as indicated. Work of the nature
shown in this illustration is blanked, drawn up and formed ready
for trimming, by means of combination tools, a typical example
of which will be found under the combination die heading on
page 5QO. The box body illustrated here as it appears before and
after trimming is shown in connection with the combination dies
as it appears in the blank, after it is formed, and after assembling
with its cover.
Triple-action Dies — These dies are used in triple-acting presses,
where in addition to
the double- action slides
which take the place of
the regular single-acting
ram, there is also a
third slide or plunger
which operates under
the table or die bed.
Thus a piece hke that,
shown which has to be
blanked, drawn and
embossed, is operated
upon from above by
the cutting and draw-
ing punches A and B,
and upon the latter
carrying the drawn
work down to the face
of the embossing die C, that die is forced upward by the plunger
D beneath and gives the piece the desired impression. On the
up-stroke of the punch the work is stripped from it by edge E and
falls out of the press.
598
DIES, PUNCH VRESS — Continued
WiringDies — Wiring
dies are much the
same in construction
as plain curling dies.
In the engraving, the
wire ring is shown at
A around the top of
the shell to be wired
and in a channel at
the top of the spring-
supported ring B. As
indicated in the lower
illustration, the punch
as it descends, de-
presses the ring B
and curls the edge of
the shell around the
wire ring A.
Disks, Reference — Accurate disks of standard dimensions for setting
calipers and measuring with. Usually of hardened steel.
Divider, Spring — The spring tends to force
the points apart and adjustments are made
by the nurled nut on the screw.
Doctor — Local term for adjuster or adapter so that chucks from
one lathe can be used on another. Sometimes used same as
"dutchman."
Dog — Name given to any projecting piece which strikes and moves
some other part, as the reversing dogs or stops on a planer or
milling machine. Sometimes applied to the pawl of a ratchet.
Dog Clamp — Grips work by clamping with the two parts of the
dog. There are many types both home-made and for sale.
Dog Lathe — Devices for clamping on work so that it can be re-
volved by face-plate. Straight tail dogs are driven by a stud on
face-plate. Curved tail (usual way) dogs have the end bent to
go into a slot in face-plate.
Bent TaU
DRAG — DRILLS 599
Drag — The bottom part of a flask, sometimes called the nowell.
Draw Bench — Place where wire is drawn from rods, being drawn
through plates or bull blocks with successively smaller openings.
Drift — A tool for cutting out the sides of an opening while driv^en
through with a hammer.
DRILLS
Center Drill — The short drills used for cen-
x cr^^^^^:^^r>0 tering shafts before facing and turning are
j)j^ called center drills. The drill and reamer
or countersink for the 60 degree center hole
^ ^^3> when combined as shown allow the center-
^ , . . ing to be done more readily than when
Combmation separate tools are used.
Core Drill — The core drill is a hollow tool which cuts out a, core
instead of removing the metal in the form of chips. Such
___^_^___^^^^^^ drills are generally used to procure a
^ ( ( I ')) core from the center of castings or
forgings for the determination of the
tensile strength or other physical properties of the metal.
Gun Barrel Drill — Gun barrel drills are run at high speed and
under very light feed, oil being forced through a hole in the drill
to clear the chips and cool the cut-
^ ^ ting point and work. The drill itself
is short and fastened to a shank of
suitable length.
Hog Nose Drill — More like a boring tool. Mostly used for boring
out cored holes. Must be very stiff to be effective but when
made right and used to advantage, does lots of hard work.
Hollow Drill — The hollow drill is for deep-hole drilling. It has
an opening through the body and is
/r-y fiV^:^^^^^^^ attached to a shank of the necessary
\i^-.l iJS-^^'^^^^===r-/ length for the depth of hole to be
drilled.
Oil-drill (Morse) — These drills convey lubricant to the point,
through holes formed in the solid metal.
Where the drills are larger than 2^
inches an inserted copper tube is em-
ployed to carry the oil to the drill point
and wash out the chips and keep the drill
cool. The oil enters through the hollow
shank or through a connection at the
side as shown.
Twist Ratchet Drill — The square taper shanks
of these drills are made to fit a ratchet
for drilling holes by hand.
Flat
I^)
6oo
DRILLS — Continued
Shell DriU — Shell drills are fitted to a taper
shank and used for chucking out cored
holes and enlarging holes drilled with
a two-flute twist drill. The angle of
the spiral lips is about 1 5 degrees.
Straight Flute Drill — The straight flute, or "Farmer" drill as it is
frequently called after its inventor, does not clear itself as well
^ as the twist drill does, but is stiffer,
& (("(_c" ■ '> and does not "run" or follow blow-
holes or soft spots as readily as the
twist drill. It is also better for drilling brass and other soft
metals.
Three and Four-groove Drills — Where
large holes are to be made in solid stock,
it is advisable to use a three or four
groove drill after running the required
two-flute drill through the piece. These
drills will enlarge the hole to the size
required and are also useful in boring
out cored holes in castings.
Twist Drill — Usually made with two flutes or grooves, running
around the body. This furnishes cut-
^ ting edges and the chips follow the flutes
out of the hole being drilled.
Wood Drill (Bit) — Bits for wood drilling
are made in various forms. The pod
drill is cut out hollow at the working
end; the double flute spiral drill has a
regular bit point; the single flute drill
is full diameter for a short distance only
and is cleared the rest of the length as
indicated.
be used in connection with a brace or
Three Groove
Four Groove
^SU
Pod
Bit Point
Single Flute
Drill, Chain — Device to
breast drill in many places where it is not convenient to bring a
ratchet drill into use.
Drill Speeder — Device which goes on drill spindle and gears up the
speed of drills so that small drills can be used economically on
large drill presses.
Drill Vise — See Vise, Drill.
1. Vertical driving-shaft gear.
2. Center driving-shaft gear.
3. Elevating tumble-plate seg-
ment.
4. Elevating-screw gear.
5. Column cap.
Drill, Radial — Parts of
6
7'
Vertical driving shaft.
Column sleeve.
8. Elevating-lever shaft.
9. Elevating screw.
10. Arm girdle.
11. Arm-binder handle.
DRILLS — Continued
60 1
RADIAL DRILL — FULL UNIVERSAL — BICKFORD
12.
Arm-miter gear guard.
3°-
Spindle sleeve.
l.v
Arm-worm box.
31-
Feed rack.
14.
Arm pointer.
32.
Spindle.
15-
Full universal arm.
33-
Saddle-binding lever.
16.
Arm-clamping nuts.
34-
Feed hand wheel.
17-
Arm-dowel pin.
35-
Head-moving gear.
18.
Arm shaft.
36.
Arm-swinging handle.
IQ.
Arm ways.
37-
Elevating lever.
20.
Arm rack.
38.
Clamping ring.
21.
Saddle.
39-
Clamping-ring handle.
22.
Reversing lever.
40.
Column.
2,S-
Back-gear lever.
41.
Column driving-miters
24.
Head-swiveling worm.
42.
Driving-shaft coupling.
2,S-
Feed-trip lever.
43-
Driving pulley.
26.
Index gear.
44.
Speed-change lever.
27.
Universal head.
45-
Speed-box case.
28.
Quick-return lever.
46.
Box table.
89.
Feed-rack worm shaft.
'47-
Base.
6o2
DRILLS — ■ Continued
DRILL PRESS —CINCINNATI MACHINE
TOOL COMPANY
DRILLS — Continued
603
Drai Press — Parts of
1.
Main driving gears, bevel.
iS.
Feed-change handle.
2.
Back gears.
19.
Sliding head.
3-
Upper cone pulley.
20.
Face of column.
4-
Yoke to frame.
21.
Back brace.
5-
Feed gears.
22.
Belt shifter.
6.
Counterweight chains.
22,-
Rack for elevating table.
7-
Feed shaft.
24.
Table-arm clamping screws.
8.
Spindle.
25-
PuUey stand.
9-
Back-gear lever
26.
Lower cone pulley.
10.
Columa
27.
Belt-shifting fingers.
II.
Automatic stop.
28.
Tight and loose pulleys
12.
Spindle sleeve.
29.
Table.
13-
Feed-trip lever.
3°-
Table-clamp screw.
14.
Hand- feed wheel.
31-
Table arm.
15-
Quick-return lever.
32.
Table-adjusting gear.
16.
Feed gearing.
33-
Base.
17-
Feed box.
34-
Ball-thrust bearing.
Drive or Force Fit — See Fit.
Dry Sand Molds — Molds made of green sand and baked dry in
ovens or otherwise dried out before pouring.
Dutchman — Local term for a wedge or liner to make a piece fit.
Used to make a poor job useable. A round key or pin fitting
endwise in a hole drilled half in a shaft and half in the piece to
be attached thereto.
Ejector — An ejector on punch press work is a ring, collar or disk
actuated by spring pressure or by pressure of a rubber disk, to
remove blanks from the interior of compound and other dies. It
is often called a shedder.
Elliptic Chuck — See Chuck, Oval.
Emery Jointer — Grinder for making a close joint between the share
and mold board of steel plows.
Emery Wheel Dressers — See Grinding Wheels and Diamonds.
End Measuring Rod — Arranged for internal measurements similar to
the internal cylindrical gages.
Expanding Arbor or Mandrel — See Arbor.
Extractor, Oil — Machine for extracting oil from iron and metal
chips. Revolves rapidly and throws out the oil by centrifugal
force.
Face Cam — See Cam, Face.
Face Plate — The plate or disk which screw^s on the nose of a lathe
spindle and drives or carries work to be turned or bored,
times applied to table of vertical boring mill.
Face Reamer — See Reamer, Face.
Some-
6o4 FEATHER — FORCE
Feather — Might be called a sliding key — sometimes called a spline.
Used to prevent a pulley, gear or other part, from turning on the
shaft but allows it to move lengthwise as in the feed shaft used
on most lathes and other tools. Feather is nearly always fastened
to the sliding piece.
Field — Usually the stationary part of a dynamo or motor.
Files — Tools of hardened steel having sharp cutting points or teeth
across their surface. These are forced up by a chisel and ham-
mer.
Filing Machine — Runs a file by power, usually vertically. Useful
in many kinds of small work.
Fin — The thin edge or mark left by the parting of a mold or die.
In drop forge work this is called the "flash."
Fit, Drive or Force or Press — Fitting a shaft to a hole by making the
hole so the shaft can be driven or forced in with a sledge or some
power press, often requiring many tons pressure.
Fit, Running or Sliding — Enough allowance between shaft and hole
to allow it to run or slide without sticking or heating.
Fit, Shrink — Fitting a shaft to a hole by making the hole slightly
smaller than the shaft, then heating the piece with the hole till it
expands enough to allow shaft to enter. When cool the shaft is
very tightly seized if the allowance is right.
Fit, Wringing — A smaller allowance than for running but so that
the shaft can be twisted into the hole by hand. Usually applied
to some such work as a boring bar in a horizontal boring ma-
chine. Sometimes used in connection with twisting two flat sur-
faces together to exclude the air.
Flask — The frame which holds the sand mold for the casting.
Includes both the cope and drag.
Flat Reamer — See Reamer, Flat.
Flatter — Round face. A blacksmith's, ,
tool which is held on the work anc|^
struck by a sledge. Used to take outi
hammer marks and smooth up a forg4
ing- ]
Flute — Shop name for a groove. Applied to taps, reamers, drills
and other tools.
Fly-wheel — Heavy wheel for steadying motion of machinery. G
an engine it carries the crank past the center and produces
uniform rotation.
Follower Rest — A back rest for supporting long lathe work; attach
to the carriage and following immediately behind the turning tool.
Foot Stock — The tail stock or tail block of a lathe, grinder, etc.
Force — A master punch which is used under a powerful press to
form an impression in a die. Forces are commonly employed in
the making of coining and other embossing dies. A similar tool
used by jewelers is called a "hub," It is sometimes referred to
incorrectly as a "bc^."
I
FORGE — GAGES
605
["orge — Open fireplace for heating metals for welding, forging, etc.
Has forced draft by fan or bellows.
Forging Press — Heavy machine for shaping metal by forcing into
dies -by a steady pressure instead of a sudden blow as in drop
forging. Similar to a bulldozer.
Tork Center — A center for driving woodwork in the lathe. Also
used in hand or fox lathes for driving special work.
Fox Lathe — Lathe for brass workers having a "chasing bar" for
cutting threads and often has a turret on the tail stock.
Franklin Metal — An alloy having zinc as a base, used for casting in
metal molds.
iFuUer — Blacksmith's tool something like a hammer, having a round
nose for spreading or fulling the iron under hammer blowers.
Hand Fuller
Furnace, Muflle — Furnace for heating steel
to harden, in which the flame does not
come in contact with the metals.
Furniture — In machine shops applies to tool racks, lathe pans, tote
boxes, etc.
Fuse — A piece of metal which melts when too much current passes
and acts as a safety valve.
GAGES
Depth Gage — A tool for measuring the
depth of holes or recesses. The body is
placed across the hole while the rule is
slipped down into the hole to be meas-
ured. In many cases the rod is simply
a wire and not graduated.
Drill Gage — Flat steel plate drilled with different size drills and each
hole marked with correct size or number.
6o6
GAGES — Continued
^ 5)
%
C- iM t) g
Feeler or Thickness Gage — Has blades of
different thicknesses, in tliousandths of
an inch, so that sHght variations can
be felt or measured.
Gear Tooth Depth Gage — A gage for meas-
uring the depth of gear teeth. Requires
a different gage for each pitch. t
Limit Gage — A plug or other gage having
one end larger and the other smaller _
than the nominal size. If the small
end of the plug goes in but the large I
end does not, the size is between the two and within the limits of
the gage. Similarly, in the case of a female limit gage, if the large
end of the gage goes over the piece of work and the small end
does not go over it, the work is within the established limits.
Ordinarily, one end of a limit gage is marked " Go," and the _
other end "Not Go," or else they are stamped + and — .
Plug and Ring Gage — Gages for use in
measuring inside and outside work or
for use in setting calipers. i^
Radius or Curve Gage — Made like a feeler or thread gage but has
each blade with a given outside radius on one end and inside ii
radius on the other for gaging small fillets or round edges.
Scratch Gage — For scratching a line at
.^■^ . a given distance from one side of
'■^ ' ' ' a piece. Adjustable for different^
lengths. ;
Snap Gage — A solid caliper used for either •
inside or outside measurement. This |
shows a combined gage for outside
and inside work. Sizes can be the same ^
or give the allowance for any kind of fit
desired.
Splining or Key-seat Gage — Gage for laying out key-seats on shafts. '
Surface Gage — A tool for gaging the hight ^
between a flat surface such as a planer
table or a surface plate and some point on
the work. This can then be transfered to
any other point. /
GAGES — GEARS
607
Thread Gage — Tool with a number of
blades, each having the same number
of notches per inch as the thread it rep-
resents. Made for different kinds of
threads and in various forms.
Wire Gage — Gage for measuring sizes
pfTTTTTinmnroTroinn^^ of wire. The wire fits between the
j sides of the opening, not in the holes.
\_J'^[J\j''JJ7JTJ"LrLrUlJ Sometimes made in the form of a
circular disk.
Worm Thread Tool Gage — For grinding thread tool for worm threads
— 29 degree angle.
Gang Tool — A holder with a number of
tools, generally used in the planer but
sometimes in the lathe. Each tool cuts
a little deeper than the one ahead of it.
GEARS
Angular Gears — Sometimes applied to bevel gears and also to spur
gears with helical or skew teeth. See those terms for definition.
Annular Gear — Toothed ring for use in universal chucks and simi-
lar places. Teeth can be on any of the four faces although when
inside it is usually called an internal gear.
Bevel Gears — Gears cut on conical surfaces to
r^l^ transmit power with shafts at an angle to
^w> each other. When made for shafts at right
angles and with both gears of the same size
are often called "miter" gears. Teeth may
be either straight, skew or herring bone.
Crown Gear — A gear with teeth on the side of rim. Used before
facilities for cutting bevel gears existed. Seldom found now.
Elliptical or Eccentric Gears — Gears in
which the shaft is not in the center.
O)) )) !^ O )) IP May be of almost any shape, oval,
heart-shape, etc. Printing presses
usually have good examples of this.
Helical Gears — Gears having teeth at an angle across the face to
give a more constant pull. Also give side thrust. More often
called "skew" teeth.
Herring-bone Gears — Gears having teeth cut
at a double angle. Made by putting two
helical or "skew" tooth gears together.
Does away with side or end thrust.
6o8
GEARS — Continued
Intermittent Gears — Gears where the teeth
are not continuous but have plain sur-
faces between. On the driven gear
these plain surfaces are concave to fit
the plain surface of the driver and the
driven wheel is stationary while the
plain surfaces are in contact.
Internal Gears — Gears having teeth on
the inside of a ring or shell.
Module or Metric Gears — French system of making gears with metric
measurement. Pitch diameter in millimeters divided by the
number of teeth in the gear.
Pin Gear — Gear with teeth formed by pins such as the old lantern
pinion. Also formed by short projecting pins or knobs and only
used now in some feeding devices.
Quill Gears — Gears or pinions cut on a quill or sleeve.
Skew Gears — See Helical.
Spiral Gears — Spur gears with spiral teeth
which run together at an angle and do th«;
work of bevel gears.
Spur Gears — Wheels or cylinders whose
shafts are parallel, having teeth across
face. Teeth can be straight, helical or
skew or herring bone.
Staggered Tooth Gears — Made up of two or more straight tooth spur
gears, teeth set so that teeth and spaces break joints instead of
presenting a continuous pull.
Worm Gears — Spur gears with teeth cut on angle to be driven by a
worm. Teeth are usually cut out with a hob to fit the worm.
GEARS — Continued
609
o
Sprocket Gears — Toothed wheels for chain
driving. A is the regular and B is a hook
tooth for running one way only.
Gear Teeth — The projections which, meshing together, transmit a
positive motion. The involute curve tooth is now almost univer-
sal. The older form has a 14^ degree pressure angle but some are
using a shorter tooth, known as a "stub" tooth, with 20 degrees
pressure angle. An involute tooth rack has straight sides to the
teeth.
Gears, Pitch of — Chorda!, distance from center of one tooth to center
of next in a direct line.
Circular, distance from center of one tooth to center of next
along the pitch line.
■ Diametral, number of teeth per inch of diameter.
Geneva Motion — A device which gives a
positive but intermittent motion to the
driven wheel but prevents its moving
in either direction without the driver.
The driver may have one tooth as shown
or a number if desired. Also made so
as to prevent a complete revolution of
the driven wheel.
German Silver — .A.n alloy of copper 60 parts, zinc 20 parts, nickel
20 parts.
Gib — A piece located alongside a sliding member to take up wear.
Gland — A cylindrical piece enveloping a stem and used in a stuffing-
box to make a tight joint.
Green Sand Molds — Molds made of sand that is moistened for
molding and not dried out or baked before pouring.
Grinder, Disk — A grinding machine hav-
ing steel disks which are covered with
emery cloth. Some disks have spiral
grooves to give cushions under the
emery cloth.
Grinder Wheel Dresser — A tool consisting of pointed or corrugated
disks of hard metal which really break
or pry off small particles of the grinding
wheel when held against its rapidly re-
/olving surface.
6io
GRINDING MACHINE
GRINDING UACnmE — Continued
6n
Grinding Machine
— Parts of
I.
Internal grinding fixture.
25-
Wheel-stand slide.
2.
Water guard supports.
26.
Footstock center.
3-
Water guards.
27.
Diamond tool-holder.
4-
Plain back rests.
28.
Footstock.
5-
Universal back rest.
29.
Tension adjusting knob.
6.
Automatic cross-feed pawl.
30-
Quick-adjusting lever.
7-
Starting and stopping lever.
31-
Clamping lever
8.
Table-reversing dogs.
32.
Clamping bolt.
9-
Headstock index finger.
33-
Table scale.
lO.
Live spindle-locking pin.
34.
Bed water guard.
II.
Live spindle-driving pulley.
35-
SUding table.
12.
Headstock.
36.
Swivel table knob.
13-
Dead center pulley.
37-
Swivel table.
14.
Work driving arm and pin.
38-
Hand wheel.
15-
Headstock center.
39-
Table travel control.
16.
Headstock base.
40.
Automatic cross-feed.
17-
Cross-feed hand wheel.
41.
Universal chuck.
18.
Reversing lever.
42.
Tooth rest.
19.
Water piping.
43-
Center rest.
20.
Wheel-driving pulley.
44.
Face-grinding chuck.
21.
Wheel guards.
45-
Face plate.
22.
Spindle box.
46.
Internal grinding counter.
23-
Wheel stand.
47-
Work-driving dogs.
24.
Wheel-stand platen.
Grinding Wheels — Common types of grinding wheels made of
^ emery, corundum, carborundum and alundum, are the disk, ring,
saucer, cup and cylinder. Disk and ring wheels are used on the
periphery; saucer wheels on the thin edge; cup and cylinder
wheels on the end. The latter are commonly used for surface
grinding. See pages 224 and 225 for other shapes.
r _
W////////A y/////////
J
\///////////A V///////////A
Disk
Cup
^^
•^^
Cylinder
Ring
Saucer or Dish
Gripe — Local name for machine clamp.
Ground joint — A joint finished by grinding the two parts together
with emery and oil or by other abrasives.
Ground — A connection between the electric circuit and the earth.
Gudgeon — Local name for a trunnion or bearing which projects
from a piece as a cannon.
6l2
GUIDE LINER — HAMMER
Guide Liner — A tool for use in locomotive
work for lining up guides and cross heads.
H
Half Nut — A nut which is split lengthwise. Sometimes half is used
and rides on screw, in others both halves clamp around screw as
in the half nut of a lathe carriage.
Hammer — The common types of machin-
ists' hammers are the ball peen, straight
peen and cross peen, as shown. The
so-called engineer's and the riveting
hammers have cross peens.
Ball Peen
Straight Peen
Cross Peen
Hammer, Blacksmith's Flatter — A flat-
faced hammer used to smooth the sur-
faces of forgings. Is held on the work
and struck by a helper with a sledge.
Hammer, Bumping or Horning — For closing seams on large cans,
buckets, etc.
Hammer, Drop — Hammer head or "monkey" or "drop" is raised
by hand or power and falls by gravity. Sometimes raised by a
board attached to top of hammer head and running between
pulleys. Others use a belt.
HAMMER— HUNTING TOOTH 613
Hammer, Helve — Power hammer in which there is an arm pivoted
in the center and power applied at the back end while the hammer
is at the other and strikes the work on an anvil.
Hammer, Lever Trip — Trips the hammer by a cam or lever and
allows it to fall.
Hammer, Spring — Comparatively small hammer giving a great
variety in the force of blow. This is controlled by pressure of
foot on lever.
Hand Wheels, Clutched — Hand wheels connected to shaft by a
clutch which can be thrown out by a knob or otherwise so that
accidental movement of wheel will not disturb setting. Used on
milling machines and similar places. .
Hanger, Drop — Shaft hanger to be fastened
to ceiling with bearing held in lower end.
Hanger, Post — Shafting hanger for fasten-
ing to posts or other vertical structures.
Hardie — Blacksmith's cutting chisel which
fits a hole in the anvil and forms the
lower tool in cutting off work.
Harveyizing — The surface hardening of steel armor plates by using
a bed of charcoal over the work and then gas turned on so it
will soak in from the top. Not adapted to small work.
Hindley Worm — See Worm.
Hoist, Chain — Hoist with chain passing through pulley block used
for hoisting.
Holder, Drill — Device for holding drill stationary while work is
revolved by lathe chuck, or face place. Not a drill chuck.
Hooks, Twin or Sister — Double crane hook which resembles an
anchor and allows load to be carried on either side.
Hub — A master punch used in making jewelry dies for fancy em-
bossing, and various forms to which articles of gold and silver are
to be struck.
Hunting Tooth — An extra tooth in a wheel to give it one^more tooth
than its mate in order to prevent the same teeth from meshing
together all the time.
6i4
IDLER — JIG
I
Idler or Idler Pulley — See Pulley, Idler.
Incandescent — A substance heated to white heat as in the bulb of
a lamp.
Indexing, Compound — Indexing by combination of two settings of
index, either by adding or subtracting.
Indexing, Differential — Indexing with the index plate geared to the
spindle, thus giving a differential motion that allows the indexing
to be done with one circle of holes and with the index crank
turned in the same direction, as in plain indexing.
Indexing, Direct — Indexing work by direct use of dividing head of
milling machine.
Indicator, Lathe Test — Instrument with multiplying levers which
shows slight variations in the truth of revolving work. Used for
setting work in lathe or on face-plate.
Plain Indicator
Watch Dial
Induction Motor — A motor which runs by the magnetic pull through
the air without contact. Usually a constant-speed motor.
J
Jack, Hydraulic — Device for raising weight or exerting pressure by
pumping oil or other liquid under a piston or ram.
Jack, Leveling — Small jacks (usually screw jacks)
for leveling and holding work on planer beds
and similar places. Practically adjustable
blocking.
Jack, Screw — Device for elevating weights by
means of a screw.
'Jack Shaft — See Shaft, Jack.
Jam Plates — Old name for screw plates and in
many cases a true one as the thread was jammed instead of cut.
Jig, Drill — A device for holding work while drilling, having bush-
ings through which the drill is guided so that the holes are cor-
rectly located in the piece. . Milling and planing jigs (commonly
called fixtures) hold work while it is machined in the milling
machine and planer. Parts produced in jigs and fixtures are
interchangeable.
JOINT — KEY
615
Joint, Universal — Shaft connection which
allows freedom in any direction and
still conveys a positive motion. Most
of them can transmit power through
any angle up to 45 degrees.
Journal Box — The part of a bearing in which the shaft revolves.
K
Kerf — The slot or passageway cut by a saw.
Key — The piece used to fasten any hollow object to a shaft or rod.
Usually applied to fastening pulleys and fly-wheels to shafts; or
locomotive driving wheels to their axles. Keys may be square,
rectangular, round or other shape and fasten in any way. Are
usually rectangular and run lengthwise of shaft.
Key, Barth — This key w^as invented
several years ago by Carl G. Barth.
It is simply a rectangular key with
one-half of both sides beveled off at
45 degrees. The key need not fit
tightly, as the pressure tends to drive
it better into its seat. As a feather
key this key has been used in a great many cases to replace rect-
angular feather keys which have given trouble. It has also been
used to replace keys w^hich were sheared off under heavy load.
Key, Center — A ilat piece of steel, with tapered sides, for removing
taper shank drills from drill spindle or similar work.
Key, Lewis — A key invented by Wilfred
Lewis' about 20 years ago. Its posi-
tion is such that it is subjected to com-
pression only.
Key, Round End — Is fitted into a shaft by
end milling a seat into which the key is
secured. Where a key of some length is
fixed in the shaft and a member arranged
to slide thereon it is called a feather or
feather key.
for cutting keyways in shafts or hubs of
Key, Taper — The taper key is made with
and without head. The taper is com-
monly I or j\ inch per foot.
Key, Woodruff — A semi-circular key
used in various kinds of shafts, studs,
etc. It is fitted in place by merely
sinking a seat with a shank mill such
as the Whitney cutter.
Key Seater — Machine
pulleys or gears.
6i6 KEYW AY — LATHE PARTS
Keyway -^ A groove, usually square or rectangular, in which the key
is driven or in which a "feather" slides. The groove in both the
shaft and piece which is to be fastened to it, or guided on it, is
called a keyway.
Knurling — See Nurling.
Land — Space between flutes or grooves in drills, taps, reamers or
other tools.
Lap — Applied to seams which lap each other. To the distance a
valve must move before opening its port when valve is central
on seat. To a tool usually consisting of lead, iron or copper
charged with abrasive for fine grinding. See Lap, Lead.
Lap Cutter — For preparing the ends of band-saws with bands for
brazing. Uses milling cutters.
Lap Grinder — This prepares the laps of band-saws by grinding.
Lap, Lead — L^sually a bar of lead or covered with lead, a trifle smaller
than the hole to be ground. Emery or some fine abrasive is used
which gives a fine surface. Laps are sometimes held in the hand
or are run in a machine and the work held stationary. Also
consists at times of a lead-covered disk, revolving horizontally,
which is used for grinding flat surfaces. Very similar in action
to a potter's wheel.
Lathe, Double Spindle — Has two working spindles, so located that
one gives a much larger swing than the other, and both can be
used to advantage. Especially good for repair shops.
Lathe, Engine — The ordinary form of lathe with lead screw, power
feed, etc.
Lathe, Engine — Parts of
I.
Rear bearing.
20.
Cross-feed screw.
2.
Back-gear case.
21.
Cross-power feed.
3-
Cone pulley.
22.
Half-nut handle.
4-
Face-gear guard.
23-
Regular power feed.
5-
Front bearing.
24.
Feed reverse.
6.
Face plate.
25-
Gear stud.
7-
Live center.
26.
Hand feed.
8.
Dead center.
27.
Front apron.
9-
Tail spindle.
28.
Rear apron.
lO.
Tail-spindle lock.
29.
Lead screw.
II.
Tail stock slide.
30-
Feed rod.
12.
Locking bolts.
31-
Feed gears.
13-
Tailstock base.
32-
Feed box.
14.
Tailstock pinion.
33-
Change gear handle
15-
Tailstock hand wheel.
34-
Compound gears.
16.
Steady rest.
35-
Change-gear handle.
17-
Tool post.
36.
Change-gear handle.
18.
Compound rest.
37.
Change-gear handle.
19.
Cross-sUde.
S8.
Bed.
LATHE — ENGINE
617
6i8
LATHE APRON
LATHE, SPINNING 619
Lathe Apron, Reed — Parts of
1. Cross-feed screw. 16. Clutch ring.
2. Cross-slides. 17, Clutch levers.
3. Wing of saddle. 18. Pinion.
4. Cross-feed pinion. 19. Gear in train.
5. Cross-feed gear. 20. Feed-clutct handle.
6. Cross-feed handle. 20A. Clutch spreader.
7. Rack. 21. Hand pinion.
8. Power cross- feed and control. 22. Carriage handle.
9. Gear in train. 2^' Lead screw.
10. Pinion for cross-feed. 24. Rack pinion knob.
11. Main driving pinion. 24A. Rack pinion.
12. Bevel gear. 25. Feed rod.
13. Bevel pinion. 26. Upper-half nut.
14. Feed- worm. 27. Lower-half nut.
15. Feed-worm wheel. 28. Half-nut cam.
Note: — Cross-feed is from bevel pinion 13, through gears 12, 11, 9,
10, and 4. Regular feed is through worm 14, worm wheel 15,
clutch 16, pinion 18, gears 19 and 2 4 A. Hand movement is through
handle 22, pinion 21, 19 and 24A.
Lathe, Extension — So made that bed can be lengthened or shortened.
When bed is made longer, there is a gap near head, increasing the
swing for face-plate w^ork.
Lathe, Fox — Brass workers' lathe having a "fox" or chasing bar for
cutting threads. The bar has a "leader" which acts as a nut on
a short lead screw or "hob" of the desired pitch (or half the
pitch if the hob is geared down 2 to i) and carries a tool along at
the right feed for the thread. Sometimes has a turret on the
back head.
Lathe, Gap — Has V-shaped gap in front of head stock to increase
swing for face-plate work.
Lathe, Gun — For boring and turning cannons and rapid-fire guns.
Lathe, Ingot — For boring, turning and cutting off steel ingots.
Lathe, Precision — Bench lathe made especially for small and very
accurate die, jig or model work.
Lathe, Projectile. — Simply a heavy lathe for turning up projectiles-
Sometimes has attachment for pointing them.
Lathe, Pulley — Especially designed for turning pulleys, can turn
them crowning or straight.
Lathe, Roll Turning — For turning rolling mill, steel mill and calendar
rolls.
Lathe, Screw Cutting — Having lead screw and change gears for
cutting threads.
Lathe, Shafting — For turning long shafts or similar work.
Lathe, Speed — A simple lathe w'ith no mechanically actuated car-
riage or attachments.
Lathe, Spinning — For forming sheet metal into various hollow
shapes, all circular. Done by forcing against a form of some
kind (with a single round ended tool) while it is revolving.
620 LATHE — LOAM MOLD
Lathe, Stone Turning — Specially designed for turning stone columns
or similar shapes.
Lathe, Turret — Having a multiple tool holder which revolves.
This is the turret. Usually takes place of tail or foot stock but
not always. Usually has automatic devices for turning turret
and sometimes for feeding tools against work.
Lathe, Vertical — Name given one type of Bullard boring mill on
account of a side head which acts very much like a lathe carriage
and does a large variety of work that would ordinarily be done on
the face-plate of a lathe.
Lathe, Watchmaker's — A very small precision lathe.
Lead — The advance made by one turn of a screw. Often confused
with pitch of thread but not the same unless in the case of a
single thread. With a double thread the lead is twice as much
as the pitch.
Level — Instrument with a glass tube or vial containing a liquid
which does not quite fill it. The tube is usually ground on an
arc so that bubble can easily get to the center. Alcohol is gen-
erally used as it does not freeze at ordinary temperatures.
Level, Engineers* — Level mounted on tripod and having telescope
for leveling distant objects.
Level, Pocket — Small level to be carried in pocket.
Level, Quartering — A tool for testing driving wheels to see if crank-
pins are set 90 degrees apart. The level
has a forked end and with the angles shown.
Placing this on the crank-pin and lining the
edge with the center of axle should bring
the bubble of level in the center. If the
same result is obtained on the other wheel
the crank-pins are 90 degrees apart.
Levers — Arms pivoted or bearing on
points called fulcrums. Divided into
three classes as showm. First has ful-
crum or bearing point between power
and weight, second has weight be-
tween power and fulcrum and third
has power between weight and ful-
crum.
Line Shaft — See Shaft, Line.
Liner — A piece for separating pieces a desired distance; also called
shim.
Live Center — See Center, Live.
Loam Mold — Made with a mixture of coarse sand and loam into a
sort of plaster which is spread over brick or other framework to
make the mold. Used on large castings to produce a smoother
finish than is to be had w^ith green sand.
(•
f
•)
Power
Fulcrum
2ud Class
Weight'*
t
(f
•
•)
klcra.
Weight *
3rd CJass
Power
(r
•
•)
'Fulcrum
• Power 1
Weight 1
MILLING MACHINE
621
M
Machinists' Clamp — See Clamp.
Magnet Electro — Usually a bar of iron having coils of insulated
wire around it which carry current. Permanent magnets are of
hardened steel with no wire or current around them.
Mandrel — See Arbor.
Marking Machine — For stamping trade-marks, patent dates, etc.,
on cutlery, gun barrels, etc. Stamps are usually on rolls and
rolled into work.
Master Die — A die made standard and used only for reference
purposes or for threading taps.
Master Plate — See Plate, Master.
Master Tap — A tap cut to standard dimensions and used only for
reference purposes or for tapping master dies.
Match Board — The board used to hold patterns, half on each side,
while being molded on some types of molding machines.
Measuring Machine — ■ Practically a large bench caliper of any de-
sired form to measure work such as taps, reamers, gages, etc.
Measuring Rods — See End Measuring Rods.
Milling Cutters — See Cutters, Milling.
MILLING MACHINE — UNIVERSAL — MILWAUKEE
622
MILLING MACHINE — Continued
Milling Machine — Universal — Parts of
I.
Column.
24.
Elevating shaft.
2.
Knee.
25-
Elevating screw (telescopic).
3.
Saddle.
26.
Saddle-clamp levers.
4-
Swivel carriage.
27.
Knee-clamp levers.
5.
Work table.
28.
Fixed vertical feed trip.
6.
Over arm.
29.
Vertical feed-trip blocks.
7*
Arm brackets (arbor supports.)
30-
Door.
8.
Arm braces (harness).
31-
Dog driver.
9-
Knee clamp (for arm braces).
32.
Change-gear bracket.
10.
Spiral dividing head.
ZZ-
Change gears.
II.
TaUstock.
34.
Index plates.
12.
Starting lever.
35-
Vise.
13-
Oil tubes.
36.
Swivel base.
14.
Cutter arbor.
37-
Universal chuck.
IS-
Speed-changing lever.
38-
Driving pulley.
16.
Feed-changing lever.
39-
Feed box.
17-
Draw-in rod for arbor.
40.
Cross and vertical feed handle.
18.
Arm-clamp screws.
41.
Table-feed handle.
19.
Table stops.
42.
Clutch-drive collar.
20.
Table-feed trip block.
43-
Interlocking lever to prevent
21.
Fixed table-feed trips.
the engagement of more than
22.
Steady rest.
one feed at a time.
22,-
Cross-feed screw.
Milling Machine — Operating tool is a revolving cutter. Has table
for carrying work and moving it so as to feed against cutter.
Milling Machine, Universal — Has work table and feeds so arranged
that all classes of plane, circular, helical, index, or other milling
may be done. Equipped with index centers, chuck, etc.
Milling Machine, Vertical — Has a vertical spindle for carrying cutter.
Milling Machine
1. Spindle drawbar cap.
2. Back-gear pull pin.
3. Spindle-driving pulley.
4. Spindle head.
5. Back-gear sliding pinion and
stem gear.
6. Spindle upper box.
6. Spindle lower box.
7. Spindle head bearing.
8. Head-feed gear.
9. Idler pulleys.
10. Standard.
11. Spindle.
12. Rotary attachment.
13. Rotary attachment feed-trip
dog and lever.
14- Rotary attachment feed clutch.
15. Rotary attachment base.
16. Table and table oil pans.
17. Rotary attachment binder.
- Vertical — Parts of
iS. Feed-trip dogs, right and left.
19. Feed-trip plate.
20. Cross-feed screw.
21. Feed-clutch lever.
22. Carriage.
23. Feed clutch.
24. Table-feed screw.
25. Rotary attachment feed gears.
26. Rotary attachment hand wheel.
27. Rotary attachment feed rod.
28. Feed-driving cone.
29. Feed bracket.
30. Universal joint.
31. Telescopic feed shaft.
2,2. Driving cone.
33. Driving pulley.
34. Knee-elevating shaft.
35. Knee-elevating telescopic screw.
36. Face of standard.
37. Base.
MILLING MACHINE —Continued 62?
MILLING MACHINE — VERTICAL — BECKER
624 MITER — PAWL
Miter — A bevel of 45 degrees.
Mold — The mold consists of the cope and the drag or nowel, with
the sand inside molded to pattern and ready to pour.
Mold Board — The board used to put over a flask to keep sand
from falling when being handled and sometimes used to clamp
on when fastening molds together.
MuflSers — Ovens or furnaces^, usually of clay, where direct heat is
not required.
Muley Belt — See Belt, Muley.
Muley Shaft — See Shaft, Muley.
N
Necking Tool — Tool for turning a groove or neck in a piece of
work.
Nose — In shop work applied to the business end of tools or things.
The threaded end of a lathe or milling-machine spindle or the
end of "hog nose drill" or similar tool.
Nowel — Same as Drag.
Nurling — The rolling of depressions of various kinds into metal by
the use of revolving hardened steel wheels pressed against the
work. The design on the nurl will be reproduced on the worL
Generally used to give a roughened surface for turning a nut or
screw by hand.
Nut, Cold Punched — A nut punched from flat bar stock. The hole
is usually reamed to size before tapping.
Nut, Hot Pressed — A nut formed hot in a forging machine.
Nut, Castellated or Castle — A nut with slot across the face to admit
a cotter pin for locking in place.
Nut Machine — For cutting, drilling and tapping nuts from a bar
or rod,
Nut Tapper — For tapping hole in nuts.
Nut, Wing — A nut operated by hand and
very commonly used where a light and
quick clamping action is required.
Nuts ~ See Bolts.
O
Ogee — Name given to a finish or beading consisting of a reverse
curve. Applied to work of any class, wood or iron.
Ohm — The unit of electrical resistance. One volt will force onep
ampere through a resistance of one ohm.
Oval — Continuously curved but not round, as a circle which naSj
been more or less flattened.
Pawl — A hinged piece which engages teeth in a gear, rack or ratchet
for moving it or for arresting its motion. Sometimes used to
PEENING — PLANER
625
designate a piece such as a reversing dog on a planer or milling
machine.
Peening — The stretching of metal by hammering or rolling the
surface. Used to stretch babbitt to fit tightly in a bearing, to
straighten bars by stretching the short or concave side, etc.
Pickling Castings — Dipping into acid solution to soften scale and
remove sand. Solution of three or four parts of water to one of
sulphuric acid is used for iron. For brass use five parts water to
one of nitric acid.
Pin, Collar — A collar pin is driven tight into a machine frame or
member and adapted to carry a roll, gear, or other part at the
outer end. It differs from the collar stud
in not having a thread at the inner end.
When drilled through the end for a cotter
pin it is known as a fulcrum pin, as it is
then especially suited for carrying rocker
arms, etc.
Pin, Dowel, Screw — Dowel pins are customarily made straight, or
plain taper and fitted into reamed holes. When applied in such
a position in a mechanism that it is impossible to remove them
by driving out, they are sometimes threaded and screwed into
place.
Pin, Taper — Taper pins for dowels and other purposes are regularly
manufactured with a taper of i inch to the foot and from f to
6 inches long, the diameters at the large
end of the sizes in the series ranging from
about j^2 to If inch. The reamers for
these pins are so proportioned that each
size "overlaps" the next smaller size by about J inch.
Pickling Forgings — Putting in bath of i part sulphuric acid to
25 parts boiling water to remove scale. Can be done in 10
minutes. Rinse in boiling water and they will dry before rusting.
Pitch — The distance from the center of one screw thread, or gear
tooth or serration of any kind to the center of the next. In
screws with a single thread the pitch is the same as the lead but
not otherwise.
Pillow Blocks — Low shaft bearings, rest-
ing on foundations, or floors or other
supports.
Pitman — A connecting rod; term used more commonly in connection
with agricultural implements.
Planchet — Blank piece of metal punched out of a sheet before
being finished by further work. Such as the blanks from which
coins are made.
Planer — For producing plane surfaces on metals. Work is held on
table or platen which runs back and forth under the tool which
is stationary.
626
PLANER — Continued
PLANER- 'Co^t^tnuea 527
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628
PLANER — Continued
Planer Centers — A pair of index centers
to hold work for planing. Similar to
plain milling machine centers.
Planer, Daniels — Wood planer with a table for carrying work under
a two-armeti knife swung horizontally from a vertical spindle.
Very similar to a vertical spindle-milling machine of the planer
type. Excellent for taking warp or wind out of lumber.
Planer, Open Side — A planer with only one upright or housing,
supporting an overhanging arm which takes the place of the
usual cross rail. Useful in planing work too wide to go in the
ordinary planer.
Planer, Radius — For planing parts of circles such as links for loco-
motive or stationary engine valve motion.
Planer, Rotary — Really a large milling machine in w^hich the work
is carried past a rotary cutter by the platen.
Planer Tools — See Tools, Planer.
Planer, Traveling Head — Planer in which %vork is stationary and
tool moves over it.
Planishing — The finishing of sheet metal by hammering with smooth
faced hammers or their equivalents.
Plate, Master — A steel plate serving as a model by which holes in
jigs, fixtures and other tools are accu-
rately located for boring. In the illus-
tration the piece to be bored is shown
do welled to the master plate which is
mounted on the face plate of the lathe.
In the master plate there are as many
holes as are to be bored in the work,
and the center distances are correct.
The plate is located on a center plug
fitting the lathe spindle, and after a
given hole is bored in the work, the
master plate and work are shifted and
relocated with the center plug in the
next hole in the plate and the corre-
sponding hole in the w^ork is then bored out. This is one of the
most accurate methods employed by the toolmaker on precision
work.
Platen — A work holding table on miller, planer or drill.
Plumb Bob, Mercury '■ — Plumb bob filled with mercury to secure
weight in a small space.
Potter's Wheel — Probably the oldest machine known. Consists of
a vertical shaft with a disk mounted horizontally at the top.
The potter puts a lump of clay in the center, revolves the wheel
with his foot or by power, and shapes the revolving clay as de-
sired. See Lap, Lead for modern application of this in machine
work.
'^
r
r
/"—I
Ltai
Face Plate
Master Plate or
Model Doweled
to Jig Jig to be
Botcd
PRESS — PUNCH
629
Press, Blanking — For heavy punching or swaging.
Press, Broaching — A press for forcing broaches through holes in
metal work. Usually cleans out or forms holes that are not
round.
Press, Cabbaging — For compressing loose sheet metal scrap into
convenient form for handling and remelting.
Press, Coining — For making metal planchets from which coins are
stamped.
Press, Double Action — Has a telescoping ram or one ram inside the
other, each driven by an independent cam so that one motion
follows the other and performs two operations for each revolution
of the press.
Press Fit — See Fit.
Press, Forcing — For forcing one piece into another, such as a rod
brass into a rod.
Press, Forging — For forging metal by subjecting it to heavy pressure
between formers or dies.
Press, Homing — For closing side seams on pieced tinware.
Press, Inclinable — One that can be used in vertical or inclined
position.
Press, Screw — Pressure is applied by screw. Heavier work is done
in this way than by foot or hand press.
Press, Straight-sided — Made with perfectly straight sides so as to
give great strength and rigidity for heavy work.
Press, Pendulum — Foot press having a pendulum like lever for
applying power to the ram.
Profiling Machine — Has rotary cutter that can be made to follow
outline or pattern in shaping small parts of machines. Practically
a vertical milling machine.
Protractor, Bevel — Graduated semicircular protractor having a
pivoted arm for measuring off angles.
Pull-pin — A means of locking or unlocking two parts of machinery.
Sometimes slides gears in or out of mesh and at others operates
a sliding key which engages any desired gear of a number on
stud.
Pulley, Gallow or Guide — Loose pulley mounted in movable frames
to guide and tighten belts.
Pulley, Idler — A pulley running loose on a shaft and driving no
machinerv, merely guiding the belt. Practically same as a "loose
pulley." '
Pulley, Loose — Pulley running loosely on shaft doing no work.
Carries belt when not driving tight (or fast, or working) pulley.
Used on countershafts, planers, grinders, etc., where machine is
idle part of time. Belt is then on the loose pulley but when
shifted to tight pulley the machine starts up. See Belt Shifter,
Friction Clutch.
Punching — A piece cut out of sheet stock by punch and die; the
same as blank.
Punch, Belt — Hollow, round or elliptical punch for cutting holes foi
belt lacmg.
630 QUADRANT — REAMERS
Q
Quadrant — A piece forming a quarter circle. A segment of a circle.
The swinging plate carrying the char^ge gears in the feed train
at the end of the lathe.
Quick Return — A mechanism employed in various machine tools to
give a table, ram or other member a rapid movement during the
return or non-cutting stroke.
Quill — A hollow shaft which revolves on a solid shaft, carrying
pulleys or clutches. When clutches are closed the quill and
shaft revolve together.
R
Rack — A strip cut with teeth so that a
gear can mesh with it to convert rotary
into reciprocating motion or vice versa.
Rack Cutter — Cuts regularly spaced teeth in a straight line. Cutting
tool is either a milling cutter or a single point tool.
Ratchet — A gear with triangular shaped teeth adapted to be en-
gaged by a pawl which either imparts intermittent motion to the
ratchet or else locks it against backward movement when operated
otherwise.
Ratchet Drill — Device for turning a drill
when the handle cannot make a com-
plete revolution, A pawl on the handle
drops into a ratchet wheel on the barrel
so that it can be turned one or more
teeth.
Recess — A groove below the normal surface of work. On flat work
a groove to allow tool to run into as a planer, or a slide to run
over as a cross-head on a guide. In boring a groove inside a
hole. If long it is often called a chamber.
Relief or Relieving — The removing of, or the amount removed to
reduce friction back of cutting edge of a drill, reamer, tap, etc.
Also applied to other than cutting tools. See "backing ofl"."
REAMERS
Reamer — A tool to enlarge a hole already existing, whether a cast
or cored hole or one made by a drill or boring bar. Reamers
are of many kinds arid shape as indicated below. Usually a
reamer gives the finishing touch to a hole.
Ball Reamer — Usually a fluted or rose reamer for making the
female portion of a ball joint. It is considered advisable to space
the teeth irregularly as this tends to prevent chattering.
Bridge Reamer — A reamer used by boiler- makers, bridge builders,
ship-builders, etc., has a straight body from A to B and tapered
end from B to C. This reamer has a
taper shank and can be used in an air
drill.
REAMERS — Continued
631
c=(E>
Flat
Fluted
Center Reamer — Center reamers, or countersinks
for centering the ends of shafts, etc., are usually
made 60 degrees included angle.
Fluted
Rose
Chucking Reamer — Chucking reamers
are used in turret machines. The
plain, fluted type has teeth relieved
the whole length; while the rose
reamer cuts only on the end as there
is no peripheral clearance. Where
possible reamers used in the turret should be mounted in floating
holders which allow the reamer to play sidewise sufiEiciently to line up
with the hole in the work which may be so drilled or bored as not to
run perfectly true prior to the reaming operation.
Chucking Reamer (Three-groove) — Spiral fluted chucking reamers
with three and four grooves are employed for enlarging cored
holes, etc. They are also made with
/ rr^^^r^^r'^C5v ^^^ passages through them and in this
^^ ji'^^^^^^^^C^I' form are adapted to operating in
steel.
Flat Reamer — A reamer made of a flat piece of steel. Not much
used except on brass work and then usually packed with wooden
strips to fit the hole tightly. Flat reamers are not much used
except for taper work.
Half-round Reamer — Used considerably in some classes of work^
particularly in small sizes and taper work when taper is slight.
Not much used in large sizes. Somewhat resembles the "hog-
nose drill" in general appearance except that this is always quite
short on cutting edge.
Hand Reamer — Reamers enlarge and
finish a hole produced by drilling,
boring, etc. The cut should be light
for hand reamers and the reamer
held straight to avoid ruining the
hole. The threaded end reamer has
a fine thread to assist in drawing the
reamer into the work. The spiral
reamer is cut left-hand to prevent its
drawing into the hole too rapidly.
Reamers are. slightly tapered at the
point to enable them to enter.
Pipe Reamer (Briggs) — Pipe reamers to
the Briggs standard taper of f-inch
per foot are used for reaming out
work prior to tapping with the pipe
tap.
Straight
Threaded End
Spiral
^ fi
j>
632
REAMERS — Continued
Shell Reamer — Shell reamers have taper
holes to fit the end of an arbor on which
they are held in the chucking machine.
They are made with both straight and
spiral flutes.
Shell Reamer (Rose) — Rose reamers cut
on the end only as there is no periph-
eral clearance. They are very ac-
curate tools for finishing holes. The
shell reamers are made with taper
holes to fit an arbor for holding them
in the turret machine.
Taper Reamer — For finishing taper holes two or more reamers are
sometimes used. The roughing reamer is often provided with
nicked or stepped teeth to break up the
chip. Taper reamers are also made
with spiral teeth. Where the taper is
Roughing slight the spiral should be left-hand to
prevent the reamer from drawing in too
Q ^ 4 fast; where the taper is abrupt the teeth,
^. if cut with right-hand spiral, will help
Finishing hold the reamer to the cut and make the
operation more satisfactory.
Taper Pin Reamer — Standard taper pin reamers are made ^-inch
taper per foot and each size in • the
series will overlap the next size smaller
by about one-half inch.
Taper Reamer (Locomotive) — Reamers
for locomotive taper pins have a taper
of Y^6 inch per foot.
Rests, Slide — Detachable rests capable of being clamped to brass lathe
bed at any desired point and usually arranged to give motion to
tool in two ways; across the bed to reduce diameter or cut-oflf,
and with the bed for turning. Invented by Henry Maudsley.
Rheostat — An adjustable resistance box so that part of the current
can be cut out of the motor.
Riddle — Name given to a sieve used in foundries for siftings and
for the molds.
Riffle — Name given a small file used by die sinkers and on similar
work.
Rivet — A pin for holding two or more plates or pieces together. A
head is formed on one end when made; the other end is upset
after the rivet is put in place and draws the riveted members close
together.
RIVETS — SAW
^33
Ct=:(t
0=;
a
0:
a
a
G
Rivets
A — Machine Head
B — Cone Head
C — Wheel Head
D — Oval Countersunk Head
E — Globe Head
F — Round Head
G — Truss Head
H— Flat Head
I — Countersunk Head
J — Bevel Head
K — Wagon-Box Head.
K
Rivet Machine — For making rivets from metal rods.
Roller Bearing — See Bearing.
Rule, Hook — Rule with a hook on the
end for measuring through pulley holes
and in similar places.
Rule, Key-seat — For laying out key-seats on shaft or in hubs.
Rule, Shrink — Graduated to allow for shrinkage in casting. Used
by pattern-makers and varies with metal to be cast.
Run — Applied to drilling or reaming when the tool shows a ten-
dency to leave the straight or direct path. Caused by one lip or
cutting edge being less sharp than the other, being ground so one
lip leads the other, or from uneven hardness of material being
drilled.
Running or Sliding Fit — See Fits.
Rust Joint — A joint made by application of cast-iron turnings mixed
with sal-ammoniac and sulphur to cause the turnings to rust and
become a solid body.
S
Salamander — The mass of iron left in the hearth when a furnace is
blown out for repairs.
Sand Blast — Sand is blovm by compressed air through a hose as
desired. Used to clean castings, stonework, etc.
Sanding Machine — A machine in which woodwork is finished by
means of rolls or wheels covered with sandpaper.
Sanding Belt — Endless belt of some strong fabric, charged with glue
and sand. For sandpapering wood held in hand or by clamps.
Saw, Band — Continuous metal band, toothed on one edge and
guided between rolls. Mostly used on woodwork, but occa-
sionally on metal work, especially in European shops.
634
SCREW MACHINE TOOLS
Saw Bench, Universal — Bench on which lumber is brought to the
saw for ripping, cross-cutting, dadoing, mitering, etc.
Saw, Cold — For sawing metal. Circular saws are generally used
though not always, band saws being occasionally employed.
^ -X, Saw, Hack — Close-toothed saw for cut-
ting metal. Usually held in a hand
frame but power hack saws are now
becoming very common in shops.
=iiXlIlCD
Scarf — The bevel edge formed on a piece of metal which is to be
lap-welded.
SCREW MACHINE TOOLS
Box Tool, Bushing — The cutters in this
tool are placed with edges radial to
the stock and may be adjusted to turn
the required diameter by the screws
in the rear. The stock is supported
in a bushing and must therefore be
very true and accurate as to size.
Box Tool, Finishing — The material
turned in this box tool is supported
by adjustable back rest jaws and the
cutters are also adjustable in and out
as well as lengthwise of the tool body.
Box Tool, Roughing — This tool has one or more cutters inverted
over the work and with cutting edges tangent to the material.
The back rest is bored out the size
the screw or other piece is to be turned
and the cutter turns the end of the
piece to size before it enters the back
rest. Sometimes a pointing tool is in-
serted in the shank for finishing the end
of the work.
Drill Holder — The end of the drill hol-
der is split and provided with a clamp
collar by which the holder is closed
on the drill.
Feed Tube — The screw-machine feed tube or feed finger is closed
prior to hardening and maintains at all times a grip on the stock.
The rear end is threaded and screwed
into the tube by which it is operated.
It is drawn back over the stock and
when the chuck opens is moved for'
ward feeding the stock the right dis-
tance for the next piece.
^BD
SCREW MACHINE TOOLS — Continued
635
Circular Dovetail
Forming Tools — Circular forming cut-
ters are generally cut below center to
give proper clearance and the tool
post is bored a corresponding amount
above center to bring the tool on the
center line. Dovetail cutters are made
at an angle of about 10 degrees for
clearance.
Hollow Mill — Usually made with 3 prongs or cutting edges and
with a slight taper inside toward the
rear. A clamp collar is used on mill
like a spring die collar and a reason-
able amount of adjustment may be ob-
tained by this collar. Hollow mills
are frequently used in place of box
tools for turning work in the screw
machine.
Nurling Tool — The two nurls in this box
are adjustable to suit different diam-
eters of work.
Pointing Tool — The bushing in this tool
receives and supports the end of the
round stock and the cutters carried in
the frame form and point the end.
Revolving Die Holder — The common type of revolving die holder
which is generally used with spring dies, has a pair of driving
pins behind the head and in the flange
of the sleeve which fits into the turret
hole. At the rear end of the sleeve is
a cam surface which engages a pin in
the shank of the head when the die
is reversed. The die is run on to the
work with the driving pins engaged.
When the work is reversed, the cam at the rear engages the pin
in the shank and holds the die from turning so that it must draw
off the work.
Spotting Tool — This tool spots a center
in the end of the bar of stock to allow
the drill to start properly, and also
faces the end of the piece true. Some-
times called "centering and facing" tool. It is desirable to have
the included angle of the cutting point less than that of the drill
which follows it in order that the latter may start true by cutting
at the comers first.
636
SCREWS
Spring Collet — Spring collets or chucks are made to receive round,
square, hexagonal or other stock
worked in the screw machine. The
collet is hardened and is closed in
operation by being pressed into the
conical cap into which it fits. When
released it springs open sufficiently to
free the stock and allow it to be fed
through the collet.
Spring Die and Extension — Spring dies
or prong dies are provided with a
collar at the end for adjusting and
are easily sharpened by grinding in
the flutes.
Screw Plates — Holders for dies for cutting threads on bolts or
screws. Dies are usually separate but sometimes cut in the
piece which forms the holder.
SCREWS
Square Head
Hexagon Head
Flat FiUister Head
Oval Fillister Head
Button Head
Countersunk Head
Cap Screws — Cap screws are machined straight from point to head,
have finished heads and up to 4 inches in length are usually
threaded three-fourths of the length. When longer than 4 inches
they are threaded one half the length, which is measured under
the head, except in the case of countersunk head screws which
are measured over all. Cap-screw sizes vary by i6ths and 8ths
and are regularly made up to i or i J inch diameter, while machine
screws with which they are frequently confused are made to the
machine-screw gage sizes.
Flat fillister heads on cap screws are often called "round"
heads; oval fillister heads are frequently designated as "fillister"
SCREWS — Continued
^37
heads, and countersunk heads as "flat" heads. When a coun-
tersunk or flat head has an oval top it is called a " French " head.
Fillister heads are also made with rounded corners as well as with
the oval head shown above. Fillister head screws are known in
England as cheese-head screws. The included angle of the
countersunk or flat head is 70 degrees.
Collar Screw — Collar or collar head
screws are used for much the same
purposes as regular cap screws, and,
in fact, are sometimes designated as
"collar" cap or "collar head" cap
screws.
Lag Screw — Lag screws, or coach screws, as they are often called,
have a thread Hke a wood screw and a square or a hexagonal
□ head. They are used for attaching
V(t1MMMl\1\^ countershaft hangers to over-head
IWVWWy*' joists for fastening machines to wood
floors and for many other purposes
where a heavy wood screw is required.
a
Fillister Head
Machine Screws — Machine screws are made
to the sizes of the machine-screw gage
instead of running like cap screws in
even fractions of an inch.
Counter Sunk or Flat Button or Round
Head
Set Screws — Set screws are threaded the full length of body and
may or may not be necked under the head. They are usually
case-hardened. Ordinarily the width of head across flats and
the length of head are equal to the diameter of the screw. The
headless set screw is known in England as a "grub" screw.
Q
Q
Flat Point
Cone Point
Round Point
Hanger Point
638
SCREWS — Continued
G
Cup Point
Low Head
e
Flat Pivot Point
Headless
Q
Round Pivot Point
Cone Point Headless
Single Shoulder
Shoulder Screw — Shoulder screws are com-
monly used for carrying levers and other
machine parts that have to operate freely.
The screw body is enough longer than
the thickness of the piece pivoted thereon
to allow the latter to work easily when
the screw is set up tight against the
bottom of the shoulder. With double
shoulders two members may be mounted
side by side and left free to operate in-
dependently of each other.
Thumb Screw — A screw with a winged or
knurled head which may be operated by
hand when a quick and light clamping
effect is desired.
Washer-head Screw — The washer formed on
this screw enables it to be used for holding
pieces with large holes without applying
a loose washer.
Wood Screws — Wood screws are made in an endless variety of forms,
a number of which are shown on the following page. They range
in size from No. o to No. 30 by the American Screw Company's
gage and are regularly made in lengths from \ inch to 6 inches.
Generally the thread is cut about seven tenths of the total length
of the screw. The flat -head wood screw has an included angle
of head of 82 degrees.
WOOD SCREWS
Flat Head
639
^
Oval Head
^
Round Head
Piano Head
t^
Felloe
jnzwttttttj^
Oval Fillister Head Countersunk Fillister Head
Clove Head
Hexagon Head
Square Bung Head
Headless
Grooved
K
Pinched Head
Round Bung Head
Winged
^'in^ed
Dowel
Drive
Winged Head
640
SCREW THREADS
Screw Thread, Acme 29 degree Standard —
no. threads per inch
d = depth = i P + -oio-
f = flat on top of thread = p x .3707
The Acme screw thread is practically the
same depth as the square thread and much
stronger. It is used extensively for lead
screws, feed screws, etc.
Screw Thread, British Association Standard —
p=pitch
d = depth=p X .6
r = radius = — —
II
This thread has been adopted in Eng-
land for small screws used by opticians
and in telegraph work, upon recom-
mendations made by the Committee of the British Association.
The diameter and pitches in this system are in millimeters.
Screw Thread, Buttress —
no. threads per inch
d=depth = f p
The buttress thread takes a bearing on
one side only and is very strong in that
direction. The ratchet thread is of
practically the same form but sharper.
Screw Thread, International (Metric) Standard—
p = pitch
d = depth=p X .6495
The International thread is of the same
form as the Sellers or U. S, Standard.
This system was recommended by a Con-
gress held at Zurich in 1898, and is much the same as the
metric system of threads generally used in France. The sizes
and pitches in the system are in millimeters.
, Screw Thread, Square —
p -^
= pitch-
no. threads per inch
d = depth = Jp
/=width of flat = Jp
s = width of space = J p.
While theoretically depth, width of
space and thread are each one half
the pitch, in practice the groove is cut slightly wider and deeper.
SCREW THREADS — Continued
64T
U--~p — 4
Screw Thread,
p= pitch =
United States Standard
I
no. threads per inch
d=dcpth==p X .6495
P_
8
f=flat=.
This thread was devised by Wm. Sellers,
and recommended by the FrankHn Institute
in 1869. It is called the U. S. Standard, the Franklin Institute,
and the Sellers thread. The advantages of this thread are, that
it is not easily injured, tap and dies will retain their size longer,
and bolts and screws with this thread are stronger and better
appearing. The system has been adopted by the United States
Government, Master Mechanics and Master Car Builders' Asso-
ciations, Machine Bolt Makers, and by many manufacturing
establishments.
r^ 2?---*l
Screw Thread, V, 60 degree Sharp —
p= pitch ^
no. threads per inch
d= depth = p X.8660
While the sharp V form gives a deeper
thread than the U. S. Standard, the
objections urged against the thread are,
that the sharp top is injured by the
slightest accident, and, in the case of taps and dies, the fine edge
is quickly lost, causing constant variation in fitting.
Screw Thread, Whitworth Standard
I
p=pitch= 7, , . ,
no. threads per mch
d=depth=p X .64033
r=radius=p x .1373
The Whitworth thread is the standard in
use in England. It was devised by Sir
Joseph WTiitworth in 1841, the system then proposed by him
being slightly modified in 1857 and 1861.
Worm Thread, Brown & Sharpe 29 de-
gree—
p = pitch =■
no. threads per inch
d = depth = p X .6866
/ = flat on top of thread = p x .335
This thread is commonly used in
America for worms. It is consider-
ably deeper than the Acme screw
thread of the same angle, namely 29 degrees.
-*\f K-
642 SECTOR — SHAPER
Sector — A device used on an index plate of a dividing "head for
indicating the number of holes to be included at each advance
of the index crank in dividing circles. The sector can be opened
or closed to form as large or small an arc as necessary to cover
the desired number of holes for each movement of the crank.
Set — The bend to one side of the teeth of a saw.
Set Screw — See Screws.
Shaft-bearing Stand — Shaft bearing which is fastened to floor.
Shaft Coupling — See Coupling.
Shaft, Flexible — Shaft made of a helical spring or of jointed parts,
usually confined in a leather or fabric casing, to transmit power
in varying directions.
Shaft, Jack — A secondary or auxiliary shaft, driven by the engine
and in turn driving the dynamos or other machinery. Jack
shafts are often introduced between a regular machine counter-
shaft and the line shaft.
Shaft, Line — The shafting driving the machinery of a shop or
section of a shop by means of pulleys and belts.
Shaft, Muley — A vertical shaft carrying two idler pulleys for carrying
a belt around a corner. To be avoided where possible.
Shaper — Work is held on table or knee and tool moves across it,
held by a tool post on the moving ram. Table adjustable for depth
of cut, etc.
Shaper — Parts of
I. Tool post.
17-
Ram guide.
2. Clapper block.
18.
Frame or body.
3. Clapper box.
19.
Feed box.
4. Clamping bolts.
20.
Feed regulator.
5. Down-feed screw.
21.
Cone-driving pulley.
6. Tool sUde.
22.
Lever bearing
7. Tool head.
23-
Power elevation of table.
8. Binder for head.
24.
Vise.
9. Stop for down feed.
25-
Swiveling base.
10. Down-feed adjustment.
26.
Table.
II. Ram adjuster.
27.
Saddle.
12. Ram.
28.
Cross-feed screw.
13. Position lever.
29.
Cross-feed dog.
14. Clamp for down feed.
30-
Cross-feed handle.
1 5 Ram slide.
31-
Elevating screw.
16. Face of column.
Shaper, Crank — Ram is driven by a crank motion.
Shaper, Draw Cut — Cutting stroke takes place when tool is mov-
ing toward frame of machine. This tends to draw the parts
together.
SHAPER — Continued
643
SHAPER — POTTER AND JOHNSTON
Shaper, Friction — Ram is driven by rack and pinion through friction
clutches. Ram is reversed by simultaneous release and engage-
ment of these clutches. These are driven by open and crossed
belts in opposite directions.
Shaper, Gear — Planes gear teeth by using a hardened cutter, shaped
like a pinion gear, and moving across the face of the gear with
a planing or shaping cut.
Shaper, Geared — Ram is driven by rack and pinion with a slow
cutting stroke and a quick return by shifting open and crossed
belts the same as on a planer.
Shapers, Traverse or Traveling Head — Ram feeds across work, which
is stationary.
Shear — Tool for cutting metals between two blades. The name
given to the way or V of a lathe or planer. A hoisting apparatus
used on wharves or docks, consisting of two heavy struts like a
long inverted V
644 SHEARS — SPRING
Shears — The ways on which the lathe carriage and tail stock move
are called "shears" by some, "ways" by others. They may be
either V, flat or any other shape.
Shears, Alligator — Name given to machine where moving knife or
cutter works on a pivot.
Shears, Squaring — Has cutter bar guided at both ends.
Shears, Slitting — Arranged for slitting sheet metal. Rotary cutters
are usually employed.
Shearing Machine — For cutting off rods, bars or plates.
Shedder — A plate or ring operated by springs or by a rubber pad
to eject a blank from a compound die. It acts as an internal
stripper, and is sometimes known as an ejector.
Sherardizing — The name given to a new process of dry galvanizii^
of any iron product.
Shifter Forks — Arms to guide belt from tight to loose pulley or
vice versa, by pressing the sides.
Shim — A liner or piece to place between surfaces to secure proper
adjustment.
Shrink Fit — See Fits.
Slip Washer — See Open Washer.
Slotted Washer — See Open Washer.
Slotter — A machine for planing vertical surfaces or cutting slots.
Tool travels vertically.
Socket, Grip — A device for driving drills and other tools with either
a straight or taper shank.
Sow — In foundry work, the gate or central channel which feeds iron
into the pigs when making pig iron.
Sow or Sow-block — Local name for a chuck for holding work, such
as dies. A ball chuck.
Spinning — The forming of sheet metal by rolling it against forms
such as lamp bodies. Lathes are made especially for this work.
Spline — Used in some sections in place of "key" and in others the
same as "feather." See Key and Feather.
Split Nut — Nut split lengthwise so as to open for quick adjustment.
Spot or Spotting — Spotting is making a spot or flat surface for a
set-screw point or to lay out from.
Spring, Compression — A helical spring
which tends to shorten in action.
Spring, Helical — A spring coiled lengthwise of its axis like a sere*
thread. Often incorrectly called a spiral spring.
Spring, Leaf — • A built up spring made of flat stock like a carriage
spring or locomotive driving spring.
Spring, Spiral — A spring wound with one
coil over the other as in a clock spring.
Usually of flat stock, but not always.
SPRING — SQUARE
645
I
Spring, Tension — A helical spring which
tends to lengthen in action.
Spring, Torsion — A helical spring which
operates with a coiling or uncoiling
action as a door spring.
Spring, Valve — A helical spring used on
valve stems and similar places; each
coil being smaller than the one below,
in order that the spring may close up
into a very small space and then have
a considerable range of action.
Spring Cotter — See Cotter.
Sprue Cutter — A cutting punch for trimming sprues from soft metal
castings.
Square, Caliper — A square with a caliper adjustment for laying out
work.
Square, Combination — A tool combining
square, level and protractor in one
tool.
Square, Center — For finding the center
of a round bar by placing across the
end and scribing lines in two diflFerent
positions. Also used as a T-square.
Not so much used as formerly.
T-Square — A straight edge with a head at one end commonly used
on the drawing board for drawing straight lines. It forms a
guide also, along which triangles are slid. Generally made of
wood, although sometimes of metal and often provided with a
swiveling head which serves as a protractor when graduated in
degrees.
Square, Try — Small square for testing
work as to its being at right angles.
646 STAND — STUD
Stand, Vise — Stand, usually of metal, for holding a vise firmly in
any desired part of the shop, making it a portable vise.
Steady Rest — A rest attached to the lathe ways for supporting long,
slender work.
Steel, High Speed — A name given to steels which do not lose their
hardness by being heated under high speed cuts. Alloy steels
which depend on tungsten, chromium, manganese, molybdenum,
etc., for their hardness.
Stocks, Ratchet — Die stocks with ratchet handles.
Straight Edge — A piece of metal having one edge ground and
scraped flat and true. Small ones are sometimes made of steel
but large, straight edges are usually of
cast iron, proportioned to resist bending,
/^[o[ O O [O O [o]^ and are used for testing the truth of flat
surfaces such as plane ways.
Strap — See Belt Polisher.
Strapping — A method of buffmg by the use of a flexible strap or
belt, usually made of cloth and covered with abrasive held in
place by glue. Runs over two pulleys or one pulley and a rod
or plate at high speed.
String Jig — Fixture for holding a row of pieces to be milled or planed.
Stripper — A thin plate placed over the die, in a punch press, with
a gap beneath to admit the sheet stock and an opening to allow
the punch to pass freely; upon the up-stroke of the punch it
prevents the strip of metal from lifting with the punch.
Stripping-plate — A plate containing holes of the same outline as the
pattern and used to prevent sand following the patterns v/hen
drawn out on some molding machines.
Stud, Collar — The collar stud forms a satisfactory device for car-
rying gears, cam rolls, rocker levers, etc.
It is often provided with a hole at the
end for a cutter pin or is slotted for a
split washer, to retain the gear, or other
part in place.
Stud, Shoulder — A stud of this form is used for mounting levers and
other parts which could be operated on a plain, unthreaded stud,
which stud, however, cannot be con-
veniently set or removed when necessary.
It is also a form of post or guide some-
times employed in machine construction
for carrying one or more sliding parts.
Stud, Threaded — Studs are threaded on both ends to lengths re-
quired and screwed tight into place. A nut is run on the outer
end. They are commonly used for
holding cylinder heads in place and
for other purposes where it is desirable
that the screw shall remain stationary
to prevent injury of threads tapped in
the main piece.
SURFACE PLATES — TAP
647
Surface Plates — Cast-iron plates have sur-
faces scraped flat for use in testing work.
Should be made in sets of three and
so scraped that each one has a perfect
bearing with the other two.
Swaging — Changing the sectional shape of a piece of metal by
hammering, rolling or otherwise forcing the particles to change
shape without cutting.
Swaging Blocks — Blocks of cast
or wrought iron to assist black-
smith in swaging and bending
iron- to various shapes. A is for
use in the hardy hole in the
anvil, B can be used anywhere
but is usually on or beside the
anvil.
Swaging Hammer — A connection with the
swaging block to swage metal to the
desired size and shape.
Swaging Machine — For reducing tapering or pointing wire or tubing
either between rolling dies or by hammering with rapid blows
between dies of suitable shape.
Sweating — Another name for soldering.
Swing of a Lathe — In the United States the swing of a lathe means
the largest diameter of the work that can be swung over the
ways or shears. In England it means the distance from lathe
center to the ways or one half the U. S. measurements.
Take-up — Name given to device for taking up slack in belt or rope
drives.
Tap — Hardened and tempered steel tool for cutting internal threads.
Has a thread cut on it and flutes to give cutting edges.
^ _ Tap, Bit-brace — Tap of any kind, usually
[^ T" D^^^^ on all bolt taps, with shank made square
to be driven by bit-brace.
Tap, Echols Thread
^mm
This form of tap has every other thread cut
away on each land, but these are stag-
gered so that a space on one land has
a tooth behind it on the next land.
This is done for chip clearance.
Tap, Hand, First or Taper — Boll tap
usually for hand use. The first or
taper tap has the front end tapered
to enter easily.
648
TAF — Continued
a
"^SOTtncn
Tap, Hand, Second or Plug — The second
tap with only a small taper to the
first two threads. Usually this tap
is the last that need be used.
Tap, Hand, Third or Bottoming — Tap
with full thread clear to the end. For
cutting a thread clear to the bottom
of a hole.
Tap, Hob for Pipe Dies — A hob tap for
cutting threads in pipe dies. Taper
I inch per foot.
Tap, Hob for Solid Dies — Used for cutting the threads in a solid
die. It is best to remove about three
fourths of the stock with a leading tap
but is not necessary.
Tap, Hob, Sellers — Has threads in center and
3 numerous flutes. For hobbing dies and
chasers.
Tap, Machine or Nut — Tap with long shank small enough to allow
tapped nuts to pass over it. After tap
is full the tap is removed from machine
and nuts slid off the shank.
Tap, Machine Screw — Taps made with
sizes and threads of machine screws.
Made with shank the size of screw
and pointed ends on small sizes.
Tap, Master — Tap for cutting solid and open dies.
Tap, Patch-bolt — Tap for boiler-makers use in patching boilers.
V ^1 (^^^ ]o( to It inches. All threads are 12 to
^ — ^^ ^::::=QSSX^^SSSSXS^mr' inch and taper is f inch per foot.
Tap, Pipe — Taper tap, f inch taper per
foot for pipe fitting.
Tap, Pulley — Tap with a long shank to
(-( ic^sassq reach the hub of pulley for tapping
set-screw holes.
Tap Remover — Device for removing broken taps. Usually have
prongs which go down in the flutes and around the central portion.
Tap, Staybolt — Tap for threading boiler sheets for staybolts. A
reams the hole, B is a taper thread, C is straight thread of right
________,,^^^ size. D square for driving tap. All stand-
^ ^ ard staybolt taps have 1 2 threads per inch.
TAP — Continued
649
Tap, Step — Tap made with "steps" or varying diameters. Front
end cuts part of thread, next step takes out more and so on to
the end. Only used for heavy threads, usually square or Acme.
Tap, Stove-bolt — Made same way as machine-screw taps but in only
six standard sizes.
Tap, Tapper — Similar to a machine tap except that it has no square
on the end.
Taper Reamer — See Reamer, Taper.
Tapped Face-plate — Having a number of tapped holes instead of
slots. Studs screw in at any desired point.
Tapping Machine — For cutting threads with taps (tapping) in nuts
or other holes.
Threads, Screw — See Screw Threads.
Threading Tool, Rivet-Dock — The tool is a
rotary cutter with cutting teeth of different
depths. The first tooth starts the cut,
then instead of feeding the carriage into
the work, the cutter is turned and the next
tooth takes the next cut.
Toggle — Arrangement of levers to mul-
tiply pressure obtained by making
movement given to work very much
less than movement of applied power.
Tongs — Tools for holding hot or cold metals.
Tool, Boring — For operating on internal surface of holes.
Tool, Cutting-off — For cutting work apart on lathe or cutting-off
machine.
Tool, Diamond — Black diamond set in metal for tracing emery or
other abrasive wheels. Also used to some extent for truing up
hardened steel or iron.
Tool Holder, Lathe or Planer — A body or shank, adopted to hold
small pieces of tool steel for cutting tools.
These can be removed for sharpening or
renewal without moving the holder and
saves resetting the tool to the work.
Tools, Inserted Cutter — Holders in which are held small steel cutting
tools. These are usually removed for grinding or replacing when
broken or worn out. Usually made of self-hardening steel.
^
650
TOOLS, LATHE
Tool, Nurling — For roughing or checking the outside of turned
work so it can be readily grasped by hand. The tool is a wheel
with the desired markings cut in the
edge and hardened. It is forced against
the work and actually forces the metal
up into the depressions in the wheel.
Most nurls are held in the end of a
hand tool but for heavy nurling they
are made to go in the tool post as shown.
TOOLS, LATHE — WM. SELLERS & CO.
Lathe
Square Thread
60°V Thread
Bent Side
Side
Bent Roughing
^ Roughing
o#«
czeC"
^
C^"
1 0
Kind
of Tool
Right
Right
Right
Right
°
1
t 1
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Square ThreEd
60 V Thread
Bent Side
Side
Nicking
Finishing
• \ N-— JO
EM"
r^"
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Kind
) (^
of Tool
Left
Left
Left
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Square Thread
Bent
CO^V Thread
Bent
Inside Bent
Bent Brass
Bent Nicking
Bent Finishing
^„
4%:
(^"
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Kind
of Tool
Right
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Left
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Left
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Square Thread
Bent
60^V Thread
* Bent
Inside Bent
Brass
Bent-Nicking
Bent Finishing
^.
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of Tool
Left ^
H
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riar
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^^
TOOL
S, LATHE
( -^
^=^
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/
Left-hand Side Tool
\
Eight-hand Side Tool
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TOOLS, hKVaS.— Continued
6Sl
Left-baud Diamond Point Eight-hand Diamond Point
Bent Eight-hand Diamond Point
Half Diamond Point. E.H.
Bound Nose.
Water Polishing Tool.
Straight Cutting-Off Tool.
Straight Threading Tool
ool. ^
Bent Cutting-Off Tool.
Bent Threading Tool.
Inside Boring Tool.
"X
^
Inside Threading Tool.
Bull Nose Tool.
Finishing or Necking Tool
1.
7^
Scaling Tool. Por Trneing Up Centers, &c.
TOOLS, PLM«:R '■■*
Left-hand Side Tool
Eight-hand Side Tool
Left-hand Diamond Point Tool.
Eight-hand Diamond Point Tool
Bull KoBe, for Heavy Guts.
Gouge Nose Tool.
652
TOOLS, PLANER — Continued
Scaling Tool.
Broad Kose or Stocking Tool.
Left-hand Siding Tool.
Eight-hand Siding Tool.
Cuttiug-Off Tool
For Finis&iug iu Coruers.
Right-hand Bevel Tool.
Left-hand Bevel Tool.
>/
For Smoothing Wrought Iron or Steel. Smoothing Tool for Cast lrx)n
TOOLS, PLANER AND BLOTTER
Blotter
Planer
Comer
a.
D-
Chamfering
Bent Finishing
Right
30 "Angle
Right
Side Finishing
Right
Finishing
Kind
of Tool
i I
I f
■i
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P
1
t
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0.
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1
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Clearance
Square
to
cr
45° Angle Slot
^^
Right & Left
Bent Finishing
Left
30 "Angle
Left
Side Finishing
p cr
Left
Splining
0-
Kind
of Tool
I
If
if
If
11
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{
Splining
so" Angle Slot
Left
45" Angle
Left
40°Angle
Left
ient Side Finishin
S p. 0
Left
; Cutting Down
Left
Kind '
of Tool
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Ueiagon
For Wrenches
SO^Angle Slot
Eight
45° Angle
Right
40':AngIe I
Right
ent Side Finishin
Right
; Cutting Down
Right
Kind
of Tool
1
!f
IP
a- P
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Clearauce
TOTE BOXES— VISE
653
Tote Boxes — See Tote Pans.
Tote Pans — Pans or trays of steel for carrying small parts from one
part of shop to another.
Train — A series of gears, as the feed train of a lathe connecting
spindle with lead screw.
Trammels — For drawing large circles.
Fit on a beam and their capacity de-
pends on the length of the beam.
Trepanning Tool — Tool for cutting an annular groove outside or
around a bored hole.
Tripper — Device that trips any piece of mechanism at the desired
time. An example is found in conveyers where the tripper
dumps the material at the desired point.
Tumbler Gear — An intermediate gear which meshes in between othet
gears to reverse the direction of the driven gear of the train.
n3^0m rotci) jM — [
Stub End ^"^^ Buckle — Turn buckles are for com
necting and tightening truss rods, tie rods,
etc., used in construction work.
(§^3(^^^|^):^)
Hook and Eye
Tuyere — The pipe or opening into forge through which air is forced.
Veeder Metal — An alloy with tin as a base, used for casting in
metal molds.
==j Vise, Chipping or Filing — Heavy bench vise
! used for holding work to chip. Vises
for filing only are similar but lighter.
Vise, Drill — Vise for use on drill press to hold work being drilled.
Vise, Hand — A small vise to be held in the
hand. For small work that requires
turning frequently to get at different
sides.
654 VISE — WRENCHES
Vise, Jig — A drill vise with arms which carry bushings so that
pieces can be drilled in duplicate without special jigs for them.
Vise, Pin — Small hand vise for holding
^ 1' ° small wire rods.
Vise Stands — See Stands, Vise.
V's — Ways shaped like a V, either raised above the bed as on a
lathe or cut below as in a planer, for guiding the travel of a car-
riage or table.
Volt — The unit of electrical pressure.
W
Washer, Open — Washers with one side open so as to be removed
or slipped under the nut to avoid necessity of taking the nut
entirely off. Also called a "C" washer.
Watt — The unit of electrical power and equals volts multiplied by
amperes. 746 watts are equal to one horse-power.
Ways — The guiding or bearing surfaces on which moving parts
slide, as in a lathe plane or milling machine. The ways may be
of any form, flat, V or any other shape.
Welding — The joining of metals by heating the parts to be joined
to the fusing point and making a union by hammering or forcing
them together. Welding in an open fire is usually confined to
iron and steel but nearly all metals can be joined in this way by
electric heating.
Wind — Pronounced with a long / as in "mind" and refers to a
twist or warping away from straightness and parallelism.
Wrench, Bridge Builders' — Large heavy wrench with a hole in end
for a tackle to apply power.
WRENCHES, MACHINE
15 degree angle wrenches have an opening milled at an angle of
15 degrees with the handle, which permits the turning of a hexagon
nut completely around where the swing of the handle is limited to
30 degrees.
22^ degree angle wrenches have an opening which forms an angle
of 22 J degrees with the handle, which permits the turning of any
square head bolt or screw completely around where the swing of the
handle is limited to 45 degrees.
Unfinished drop-forged wrenches are plain forgings, with openings
milled to fit the nut or screw on which they are to be used.
Semi-finished wrenches are milled to fit the nut or screw on which
they are to be used and case-hardened all over.
Finished wrenches are milled to fit the nut or screw on which they
are to be used and are ground, polished, case-hardened all over, lar-
quered, with heads bright.
Single End, Hex.
Double End, Hex.
WRENCHES — Cotainued
)
655
15° Angle, Single End
15° Angle, Double End
22^° Angle, Double End
S — 22^° Angle
Single End, Set Screw and
Machine
Double End, Set Screw
and Machine
''Box "-Tool Post
Double End, Tool Post
Hex. Box, 15° Angle
Chuck
Pin-face, For Round
Nuts Having Holes in
their Face to Receive
the two Wrench Pins
J
Hook Spanner, Milled
out to suit Round Nuts
Having Notches in the
Periphery to Receive
the Hook at the End of
Spanner
^
Pin Spanner Used on
Round Nuts which
have Holes in the Per-
iphery to receive the
Spanner Pin
Socket
656
WRENCHES — Continued
WRENCHES, MISCELLANEOUS
XC=ZJ>
Monkey or Screw
Pocket Adjustable
General Utility
Stillson Pipe
2:
Construction
Vulcan Chain Pipe
Pipe Tong
Track
Wrench, Tap — Wrench for holding and
turning taps. Usually made adjustable
for different sizes.
Wringing Fits — See Fits.
INDEX
Abrasives, commercial 208
Abrasive wheels, grading 222
Accurate taper gage 341
Acme, tap threads, 29 deg 25
Acme threads, 29 deg., measuring. . . 38
Acme 29 deg. screw and tap threads,
wires for measuring 38
Acme 29 deg. screw thread and B. &
S. worm thread compared 10
Acme, 29 deg. screw threads 24
Acme, 29 degree standard screw
thread 10
Addendum of gear teeth 93
A. L. A. M. horse-power rating 421
A. L. A. M. screws and nuts 306
Ahgning shafting by steel wire 428
Aligning wire, sags of steel for shaft-
ing 428, 429
Allowances for bolt heads and up-
sets _ 399
Allowances for fits, metric 325
Allowances for ground work for vari-
ous classes of fits 324
Allowances for drive fits 320, 323
Allowances for grinding 216
Allowances for grinding, table of . . . 217
Allowances for hand fits 320, 323
Allowances for press fits 320, 323
Allowances for punch and die work 270
Allowances for shrink fits 322
Allowances for threading in screw
machine 249
Allowances in shop gages for various
classes of fits 322
Allowances, lathe work for grinding 218
Allowances over standard for driving
fits 323
Allowances over standard for force
fits 323
Allowances for push or key fits 323
Alloys, bismuth 456
Alloys, brass 457
Alloys, carbonizing different 448
Alloys for coinage 455
Aluminum bars, weight per linear
foot 417
Aluminum, properties of 458
Aluminum, soldering 92
Aluminum, working 459
Alundum 208
Angle of dividing head for milling
side teeth in cutters 202
Angle of heli.x for screw-threads, table 4, s
Angles, calculation 520-525
Angles, corresponding to given tapers
per foot 361
65
PAGE
Angles, laying out by table of chords
387-389
Angles, obtained by opening two-foot
rule 403
Angles of gear teeth, finding face and
cutting 122
Angles of screw threads, table 4
Angles of V-tools, measurements for 13
Angles, sides and sines, tables of 302-397
Angles, tables for indexing in mill-
ing 190-191
Angles, tool for laying out accurately 368
Angular cutters, cutters for fluting 194
Angular cutters, number of teeth in. 194
Annealing steel 446
Antimony, properties of 458
Arcs, circular, lengths 398
Area of fillets, table of 404
Areas and circumferences of circles,
I to 1000 502-513
Armor plate, harveyizing 448
A. S. M. E. standard machine screws
290, 293
A. S. M. E. standard machine screw
heads 296-299
Automatic screw machine tools,
speeds and feeds. (See Screw Ma-
chine) 245-265
Automobile spline fittings, broaching
standards for 277-278
B
Babbitt 457
Ball bearings, combined radial and
thrust. 384-385
Ball bearings, self-aligning radial . . . 386
Ball bearings, radial 381
Ball bearings, thrust collar 382, 383
Ball handles . 37S
Ball handles, single-end 376
Ball lever handles 376
Bars, brass, copper and aluminum,
weight per linear foot 417
Bars, steeland iron, weight per linear
foot 416
Barth key 334
Baths for hardening steel 446
Baths for heating steel 444
Bearing metal 456
Bearings, combined radial and thrust
384, 385
Bearings, cooling hot 405
Bearings, self-aligning radial 386
Bearings, radial 381
Bearings, thrust collar 382', 383
Bell metal 457
7
658
INDEX
PAGE
Belt contact, factors for .r. ....... . 423
Belt fastenings ^ 426
Belt hooks 426
Belts, horsepower and shafting . .420-443
Belts, lacing 426, 427
Belts, leather, driving power of ... . 422
Belt speeds 424
Belt studs 426
Belt widths 424
Benches, types of work ; . . . 84-85
Bevel gears 121
Bevel gears, cutters for 1 21-12 2
Bevel gears, laying out 121
Bevel gears, table of 124-125
Binder handles 375
Binding screw 371
Birmingham or Stubs' iron wire gage
sizes 415
Bismuth alloys 456
Bismuth, properties of 458
Blake belt studs 426
Blanks, shell diameters, tables of 268-269
BIanks,-shell, finding diameters of. . 266
Block and roller chain sprocket
wheezs . .r..«iio ..^- ■ ■ ■ 118-11Q,
Block indexing in cutting gear teeth iij
Board feet in pieces i to 24 in. wide
up to 24 ft. long, table 402
Boiler punch and die work, clearance
for 271
Boiler rivet heads 314
Bolt circles, spacing 523
Bolt cutters, power required by ... . 438
Bolt diameters and threads, stove. . 305
Bolt heads and nuts, S. A. E 306
Bolt heads and nuts, stock required
for mfrs. standard 400
Bolt-heads and nuts, stock required
for U. S. standard 401
Bolt heads and upsets, allowances for 390
Bolt heads for standard T-slots 308
Bolt heads, Whitworth standard,
hexagonal 303
Bolts and nuts, planer head 307
Bolts and nuts, U. S., finished heads
and nuts 281
Bolts and nuts, U. S., rough 280
Bolts and nuts, U. S. standard 279
Bolts, button head machine and loom 304
Bolts, carriage 304
Bolts, countersunk head, round and
square 305
Bolts, coupling . 307
Bolts, eve 309
Bolts, hook 378
Bolts, length of 304
Bolts, machine, with mfrs. standard
heads 282
Bolts, names and descriptions. . 567-570
Bolts, nuts and screws 279-315
Bolts, tap 305
Bolts, U. S. standard, strength of 279
Bone, powdered, for carbonizing. . . . 449
Boring machine, horizontal, diagram
and parts of 57i
Boring machines, horizontal, power
required by 436
PAGE
Boring mill, diagram and parts of . . . 573
Boring mills, vertical, power re-
quired by 436-
Box tool, finish, screw-machine
speeds and feeds. 26?
Box tools for screw machine, finish-
ing 245
Box tools for screw machmes, rough-
ing 24s
Brass 457'
Brass alloys 457
Brass bars, weight per linear foot. . . .417
Brass, cast, properties of 458
Brass plates, weights of. . ._. 412-413
Brass tubing, seamless, weight of . . . 419
Brass wire 457
Brass wire, weights of 414-415
Briggs pipe joints 46 •
Briggs pipe taps 73
Briggs pipe threads, table of 47
Briggs standard pipe ends, drill sizes
for 45
Briggs standard pipe ends, gages ibrFf^ 46
Briggs standard pipe thjeada - .42
Brinell hardness test. . T. -jfT.t^. 458T'-4«3:
British association screw -threads,
table of 19
British standard pipe threads 44
Britannia 457
Broaches and broaching 273-278
Broaches for automobile spline fit-
tings 277-278
Broaches for round holes, 274
Broaches for square holes 273
Broaches, tooth spacing. . 273, 275, 276
Broaches for transmission gears 276
Broaching, application of 273
Broaching square holes, saving time
in 275
Bronze 457
Bronze, properties of 458
Bronzes, composition of 456
Brown & Sharpe micrometer readings
for Whitworth threads 28
Brown & Sharpe tapers, standard 346-347
Brown & Sharpe thread micrometer
readings, for U. S. threads 26
Brown & Sharpe thread micrometer
readings for V-thread 27
Brown & Sharpe 29-deg. worm
threads, table of 39
Brown & Sharpe worm thread and
Acme screw thread compared .... 10
Buffing wheels, speeds of 230
Bulldozers, power required by 438
Bushings, drill 369, 370
Bushings, for jigs, fixed 369. 37©
Bushings, for jigs, loose 369, 370
Button head cap screws 287
Button head machine and loom bolts 304
C
Calipering and fitting 316-340
Calipers, axial inclination of in
measuring for shrink or press fits 329
Caliper, screw thread micrometer ... 28
INDEX
659
PAGE
Calipers, side play in boring holes. . . 330
Calipers, side play of in measuring
for running fits 328, 330
Calipers, various types 574-575
Cams, cutting screw machine 155
Cams, method of laying out 152
Cams, milling by gearing dividing
head. 153
Cams, milling heart-shaped 152
Cap screws, button head 287
Cap screws, flat and oval countersunk
head 287
Cap screws, fillister head 285
Cap screws, fillister head, flat, round
and oval 286
Cap screws, hexagon and square
heads 284
Carbonizing materials 449
Carbonizing, rate of 448, 449, 450
Carbon penetration in different alloys 448
Carborundum 208
Carriage bolts 304
Case hardening steel 448
Cast gear teeth 102
Castings, shrinkage of 458
Castings, weight of in proportion to
patterns 403
Cast iron, properties of 458
Cast iron soldering 89
Cast iron washers 311
Castle nuts, S. A. E 306
Cast steel properties of 458
Centigrade and fahrenheit scales. . . 455
Chains and ropes, safe loads for. . . . 469
Change gears for cutting diametral
pitch worms in the lathe 9
Change gears for cutting screws, how
to find 3
Charcoals for carbonizing 449
Check nuts, cold punched, hexagon 300
Chip breakers for milling 145
Chordal pitch 93
Chords, table for laying out holes in
circles 390-391
Chords, table of 388-389
Chords, use of for laying out angles. 387
Chromium, properties of 458
Chucking reamers, rose, cutter for
fluting 198
Chucks, feed, screw-machine, harden-
ing 260
Chucks, magnetic 228
Chucks, various types 578
Circle, properties of 527
Circles, areas and circumferences, i
to 1000 502-513
Circles, circumferences and diameters,
I to 200 514
Circles, spacing holes in, tables for . 390
Circles, tables of sides, angles and
sines 392-397
Circular arcs, lengths of 398
Circular forming tool diameters,
tables of B. & S. screw-machine
256-259
Circular forming tool for conical
points 254
PAGE
Circular forming tools, screw ma-
chine..... 251-253
Circular pitch 93
Circumferences and areas of circles,
I to 1000, 502—513
Circumferences and diameters of
circles, i to 200 514
Circumferences of grinding wheels,
table 221
Circumferential distances, divisions
corresponding to 201
Circumferential speeds, tables of
431—437
Clearance for punch and die work 271
Clearance of gear teeth 93
Clearance of thread tool at side,
finding 4
Clearances for running fits 323
Clearances for grinding reamers 237-239
Clearance with cup and dish grind-
ing wheels 240
Coach and lag screws 312
Coach and lag screw thread lengths 312
Cobalt, properties c^ : . . . . 458
Coinage alloys -^, 455
Cold punched check and jam nuts,
hexagon 300
Cold punched nuts, mfrs. standard. . 302
Cold-saw cutting-off machine speeds
203-204
Cold-saw cutting-off machine teeth 203
Cold saws, power required by 438
Cold soldering 90
Collar-head jig screws 370
Collar head screws 285
Collets, screw machine spring, har-
dening 260
Collets, spring, hardening 260
Comparison of wire gages used in the
United States 407
Complementary angles 522
Composition of bearing metals 456
Composition of bronzes 456
Composition of steel, effect on har-
dening 451
Compound gearing, train for screw
cutting 2
Computing tapers, table for. . . . 362-363
Concave and convex cutters, cutter
for fluting 194
Concave and convex cutters, number
of teeth in 194
Constants for cutting time, table
of 205
Contact of belts, factors for 423
Conversion factors, English and
metric 476
Conversion table, English and metric 475
Cooling hot bearings 40S
Cooling steel 445
Copper bars, weight per linear foot 417
Copper plates, weights of 412-413
Copper, properties of 458
Copper tubing, weight of 419
Copper wire, weight of 414-415
Corner rounding cutters, cutters for
fluting 194
66o
INDEX
PAGE
Corner rounding cutters, number of
teeth in 194
Corner, square, laying out 405
Corundum 208
Co-secant of angle 521
Co-secants and secants, table of . 562-563
Co-sine of angle 521
Co-sines and sines, table of 540-551
Co-tangent of angle 521
Co-tangents and tangents, table of
529-540
Cotters, sprmg 309
Counterbores with inserted pilots . . . 379
Counterboring speeds in screw-
machine 265
Countersunk head bolts, round and
square 305
Couphng bolts 307
Coupling, national standard hose ... 50
Co-versed sine of angle 521
Cranes and hoists, motor require-
ments for 439
Cubes, squares and roots of fractions
1/64 to I in 490-491
Cubes, squares and roots of numbers,
I to 1000 492-501
Curves, finding radius without center 526
Cutter dimensions for B. & S. screw
machines 256
Cutters for box tool, radial 245
for box tools, sizes of steel
for 245-246
for spur gears loi
keyway dimensions 199
mUling cutters for fluting
193-194
number of teeth m 192-194
T-slot, dimensions of 200
various forms, 581-587
Whitney, for Woodruff keys 336
Cutting diametral pitch worms in
lathe 8
double threads 7
fractional threads i
lubricants for various ma-
terials 207
multiple threads : . . 6
multiple threads, face-plate
for 8
quadruple threads 7
screw threads 1-4
speeds and feeds for gears 140
speeds and feeds for screw-
machine work 261-265
speeds for cold-saw cutting-
off machine 203
speeds for screw-machine
brass stock 261
speeds for screw stock 261
speeds of planers 399
speeds, rotary in turning and
boring 206
threads with compound
gearing 2
threads with simple gearing . 2
time for boring and turning . . 205
triple threads 7
PAGE
Cutting-off cold-saw machine lubri-
cant 203
Cutting-off machine, cutting-off
speeds 203-204
Cyanide of potassium for carboniz-
ing 449
Cycloidal gear teeth 93
D
Decagon, properties of 525
Decimal equivalents of fractions of
an inch 479
Decimal equivalents of millimeters
and fractions 476
Decimal equivalents of squares,
cubes, roots, etc. of fractions . . 490-491
Decimal equivalent tables 476-484
Decimals of a foot, equivalent in
inches 486-487
Dedendum of gear teeth 93
Definitions of machine shop terms
T^ u. • J ,- . 564-656
Degrees obtamed by openmg two-
foot rule 403
Depth of keyways, finding total. 338, 339
Depth to drill and tap for studs .... 308
Depth of thread, double 65
Diagonal of bars, finding 522
Diameters and circumferences of cir-
cles, I to 200 514
Diameters of B. & S. circular form-
ing tools, tables. . . 256-259
circular forming tools
, 250-252
circular forming tools
finding 255
five pitch screw-threads,
measuring 36
shell blanks 266-267
shell blanks, tables of
268-269
Diametral pitch 93
Diametral pitch worms, cutting 8
Diamond lap for small drills 235
Diamond laps 235
Diamond lap tools 236
Diamond powder 234
Diamond powder, settling in oils 235
Diamond powder, tools for charging . 236
Diamond powder, used in boxwood
.laps 236
Diamonds, setting 219
Diarnonds, using on wheels 218
Dictionary of machine shop terms
Die clearance, punch and 271
Die for Briggs standard pipe 46
Dies and taps, screw machine 247
Dies, drop-forging, draft in 461
Dies, punch press, various t3T)es of
588-598
Dies, spring, sizes of screw machine . . 248
Differential indexing on milling ma-
chines, tables for 168-171
Dividing head, gearing for plain and
differential indexing 168-171
INDEX
66i
PAGE
Dividing head, milling cams by set-
ting 153
Dodecagon, properties of 525
Double threads, cutting 7
Double depth of threads 65
Dovetail forming tools 251
Dovetails and tapers 341-367
Dovetail slides and gibs, dimen-
sioning 364, 365
Dovetails, measuring external and
internal 366
Dovetails, measuring with plugs in
angles. 366, 367
Dowel pins, drills for 64
Dowel pins, reamers for 64
Drawing room and shop standards
369-404
Drill and wire sizes arranged consec-
utively 408-409
Drill bushings 369, 370
Drill bushings, for jigs, fixed. . . 369, 370
Drill bushings, for jigs, loose 369
Drill end lengths 68
Drilhng for studs, depth of 308
Drilling cast iron, torque required in 54
Drilling machine, radial, diagram
and parts of 601
Drilling machines, various types,
power required by _. . 437i 438
Drilling machine, vertical, diagram
and parts of 602
DriUing speeds and feeds in screw
machines 264
Drill jig screws, binding 371
collar-head 370
headless 371
locking 371
nurled-head 372
square-head 371
supporting 371
winged 370
Drill jigs, straps for 372
Drills for Briggs pipe reamers 45
dowel pins 64
drive fits 64
running fits 64
taps 62-66
Drill sizes for pipe 45
Drills, see twist drills 51-66
Drill sizes for taper pins 358
Drills, twist 51-66
Drills, various types of 599-600
Driving of machines, group 441
Driving machines, power required
for 442-443
Drop forging and steam hammers
460-463
Drop-forging dies, draft in 461
E
Electrical power 420
Emery 208
End mills, taper shank 14S
English and metric conversion table. 475
English weights and measures . . .470-471
Equivalents, decimal, squares, cubes,
roots, etc., of fractions 490-491
PAGE
Equivalents of inches in decimals of
a foot 486-487
Equivalent of inches in millimeters
477-478
Equivalent tables, decimal 476-488
Erecting perpendiculars by triangles . 387
Estimating lumber in patterns 403
Eye-bolts 309
Eye-bolts, safe loads for 469
F
Face-plate, multiple thread cutting . 8
Fahrenheit and centigrade scales 455
Fastenings, belt 426
Feather keys, square, sizes 334
Feeds of drills 53-54
Feet, board, in pieces up to 24 ft.
long, I to 24 in. wide, table 402
Files 78-83
Files, die sinkers or riffles 83
efficiency of 82
measurement of 78
sizes and shapes 80-81
test of 82
Filing, height of work for 78
Fillets, weight, area and volume of. 404
Fillister head cap screws 285
Fillister head cap screws, flat, round
and oval 286
Fillister head machine screws, Amer.
Screw Co 289
Fillister head machine screws, A. S.
M. E., oval 296
Fine pitch screw thread diameters,
measuring 36
Finishing box tool for screw machine 245
Finishing box tool for cutting speeds
and feeds 262
Fits, allowances for all classes, metric 325
Fits, allowances over standard for,
driving, force, keying or push 323
Fits, clearances for running 323
for groundwork, various classes 324
for wheel hubs, press 327
limits for drive 320, 323
for hand 320, 323
for press 320, 323
for running 321, 323
in shop gages for . . 322, 323
parallel, close 319, 320
drive 319, 320
hand 319,320
press 319, 320
running 319, 321
press and running .319-331
running, for power transmission
machinery _. .•■••.•• 32?
running, side play in caUpering
for 328, 330
Fixed bushings for drill jigs .... 369, 370
Flat and oval countersunk head cap
screws 287
Flat bar steel, weight of 418
Flat fillister head machine screws,
A. S. M. E 297
Flat head machine screws, A. S. M. E . 298
Flat on thread tools, grinding 13
662
INDEX
Fluting cutters for hobs 196
for milling cutters
193-194
for reamers 197
for taps 195
Fluxes, see soldering 86-92
Foot, decimal parts of in inch equiva-
lents 486-487
Forged and hot pressed nuts, mfrs.
standard 301
Forging, drop 461-463
Forming tool, circular for conical
points 254
circular, screw ma-
chine 251
diameters and depths 250
finding. . . . 255
dovetail, screw-ma-
chine 251
Forming tools, diameters of circular
for B. & S. screw machines,
tables 256-259
Forming tools, circular, diameters
of. 251, 252
cutting clearances of. 251
depths of... 253
screw machine. . . 251-259
speeds and feeds .... 263
Formulas for horse-power require-
ments for machines 443
Fractions, decimal equivalent tables
476-484
Fractions, prime-number, table of . . . 485
French (metric) standard screw
threads, table of 20
Furnaces for steel treatment, gas. . . 445
Furnaces for steel treatment, liquid 444
Fusible metals 456
Gage, accurate taper 341
Gage for laying out angles accurately 368
Gage for machine and wood screws 311
Gage, taper, applications of 342
Gage, taper, appHcations of formulas
for using 343-345
Gage, taper, formulas for using. .... 343
Gages, for Briggs standard pipe. ... 46
for pipe, Briggs standard. . 49
plug, standard dimensions. . . 380
ring, standard dimensions. . . 380
shop, limits in for various
kinds of fits 322, 323
sizes of wire 406--419
Stubs' wire 406
twist drill and steel wire. . 406
various types of 606-607
wire and drill, sizes arranged
consecutively 408-409
wire, different standards used
in U. S 407
Gas engine horsepower 420
Gas, casehardening with 448
Gear blanks, laying out 103
sizes of 109
tables of 109-110
(Jear cutters, power required by ... . 438
PAGE
Gearing 93-136
chordal 97
circular pitch 94
compound for screw cutting 2
constants for chordal pitch 97
corresponding diametral and
circular pitches 96
diametral pitch 95
face of worm 137
finding pitch diameter 138
for cutting diametral pitch
worms 9
metric pitch 117
module 117
simple for screw cutting ... 2
single curve tooth 106
spiral, real pitches of. . . 131-133
spiral, rules for 127
spiral, table of 126
spur gear cutters for spiral 136
standard tooth 107
stub tooth 107
stub tooth dimensions. Fel-
lows 108
worm 137
worm, proportions of 139
Gear pressure angles 106
Gears and pulleys, speeds of 430, 431
Gears, bevel 120
cutters for 1 21-122
table of 124-125
block indexing for 115
block indexing, table for 116
cutters for involute 115
for screw cutting 3
miter, table of 123
pitch diameters of 111-114
speeds and feeds for cutting. . 140
spiral, figuring 128-130
spiral, 45-deg., laying out 127
spiral, table of 134-13S
sprocket 118
spur, cutters for 136
various types of 607-608
with cast teeth 102
Gear teeth 93
Gear teeth, actual sizes of 105
Gear teeth angles, face and cutting. . 122
Gear tooth parts, proportions. . . .98-101
German threads, Loewenherz 22
German silver 457
Gold, properties of 4S8
Graduations on micrometer 318
Graduations on ten-thousandth mi-
crometer 318
Graduations on vernier 316
Grinders, various types, power re-
quired by 437
Grinding allowances 216
for lathe work . 218
for various
classes of fits. 324
table of 217
Grinding and lapping 208-244
Grinding flats on thread tools 13
Grinding flats in U. S. form of thread
tool 14. IS
INDEX
663
Grinding hardened work 216
machine, diagram and parts
of 610
reamers and cutters . . . 237-230
use of water in 218
wheel contact 214-215
circumferences, table 221
wheels and grinding 208
care of 228
combination grit . . 212
cup, clearance table
for 240
disk, clearance table
for 240
dressing with dia-
monds 218
elastic 210
grades for different
kinds of work. . . 223
grading 211,222
grain and grade . . . 209
grit and bond 208
hard 212
mounting 226
pressure and wear . . 215
shapes of 224-225
sharpening 214
silicate 211
speed of 213
speeds, table 220
spindle sizes for . . . 227
thickness of 209.
vitrified 210
Group driving of machines 441
Gun metal 457
H
Hammers, hand, various types of 612
power required by 438
steam, and drop forging
46o-4()3
capacities 460
Hand fits, limits for 320, 323
Handles, ball 375
ball lever 376
ball, single-end 376
binder 375
for hand-wheels 374
machine 377
Hand taps 71
Hand-wheel handles 374
Hand wheels, dimensions 373
Hardened work, grinding 216
Hardness test, Brinell 452, 453
Hardness test, scleroscope 454
Hardening screw machine spring col-
lets and feed chucks 260
Hardening steel 444-447
Harveyizing process for steel 448
Headless jig screws 371
Heads, key, proportions of 337
Heads of bolt, stock required for 401
Heart-shaped cams, milling 152
Heat treatment of steel 444-447
Heating steel in liquids 444
Heating steel, methods of 444
Heptagon, properties of 525
Hexagon cap screws 284
Hexagon, properties of 528
Hexagon, stock, brass weight of . . . . 417
Hexagon, steel weight of 416
High-speed steels 447
Hight of work for filing 78
Hobs for worm threads] 138
Hobs, worm wheel 41
Hob taps ,', 76
cutter for fluting ..." 196
number of flutes in 196
Sellers 76
Sellers, cutter for fluting. . 196
Holes in circles, tables for spacing
390—391
Hollow mill dimensions, screw ma-
chine... 247
Hollow mills for screw machines . 246-247
Hooks, belt 426
Hook bolts 378
Horse-power, belts and shafting . 420-443
definition 420
for machines 442,443
of steel shafting 430
rating, S. A. E 421
requirements of ma-
chine tools 436-440
steam engine 420
Hose coupling, national standard ... 50
Hot bearings, cooling 405
Hot pressed and cold punched nuts,
U. S. standard 300
Hot pressed and forged nuts, mfrs.
standard 301
Hot pressed nuts, hexagon, mfrs.
standard 301
Hot pressed nuts, narrow gage 303
Hubs, press fits for wheel 327
Hydraulic presses, power required
by 438
Imperial wire gage sizes 407
Inclination of calipers in measuring
for shrink or press fits 329
Indexing milling machines, plain and
differential 168-171
Indexing tables for plain and differen-
tial milHng 172-189
Inserted tooth cutters, number of
teeth in 192
Integral right-angled triangles 387
International standard screw threads 21
Involute gear tooth 93
Iridium, properties of 458
Iron bars, weight per linear foot 416
Iron, cast, properties of 458
Iron plates, weights of 411-413
Iron wire, weight of 414-415
Iron, wrought, properties of 458
Jam nuts, cold punched, hexagon . . . 300
Jarno tapers 355
Jig bushings, fixed 369
664
INDEX
PAGE
Jig parts, standard 369-372
screws, binding 371
headless 37i
collar-head 370
locking 371
nurled-head 372
square-head 371
supporting 371
winged 370
Jigs, laying out by trigonometry 523
Jig straps 372
Joints, Briggs pipe 46
K
Key heads, proportions 337
Keys, amount of taper for various
lengths 340
and cutters, Whitney 336
• and key -seats, dimensions 332
Barth 334
feather 334
machine, various types of 615
straight 333, 334
tapers for 340
Woodruff 336
Key system, Pratt & Whitney 335
Keyway depth, total, finding. . . .338, 339
Knobs, dimensions 374
Knots, various types 464-468
L
Lacing belts 426, 427
Lag and coach screws 312
Lag screws, length of thread on 312
Lag screw test 312
Lapping 231-236
Lapping flat surfaces 231
Lapping lubricants 332
Lapping plate for flat work 231
Lapping, pointers on 233
Laps, abrasives for 234
adjustable 233
diamond 235
for holes 232
for various kinds of work 234
internal 233
lead, advantages of 233
Lathe, engine, diagram and parts of
616-617-618
Lathes, axle, power required by 436
Lathes, cylinder, power required by 436
Lathes engine, power required by. . . 436
Lathes, wheel, power, required by . . . 436
Lathe tools, various forms of. . . .650-651
Lathe tool tests 206
Laying out angles accurately, tool
for 368
Laying out angles by table of chords 387
Laying out a square corner 405
Laying out holes in circles, tables for
390-391
Lead bath for steel 445
Lead, properties of 458
Leather belts, driving power of 422
PAGE
Leather, charred, for carbonizing 449
Length of bolts 304
Lengths of circular arcs 398
Lengths of threads cut on bolts 304
Lengths of threads cut on lag screws 312
Lever handles, ball 376
Limits for drive fits 320, 323
fits of all classes, metric. . 325
ground work for various
classes of fits. 324
hand fits 320, 323
press fits 320, 323
running fits 321, 323
shop gages for various
classes of fits 322, 323
shrink fits 322
Limits in plug gage for standard
holes. 322
Linear pitch of racks 93
Linear, square and cubic measure,
English 470
Linear square and cubic measure,
metric 474
Lining bushings for jigs 369
Locking jig screws 371
Loom bolts, button head 304
Loose bushings for drill jigs 369
Lubricants for cold-saw cutting-off
machine 203
cutting various ma-
terials 207
lapping 232
press tools 272
working copper, brass,
steel, etc. in the
punch press 272
Lubrication in milling steel 147
Lumber in patterns, estimating 403
M
Machine and wood screw gage sizes 311
bolts, button head 304
bolts, with mfrs. standard
heads 282
handles 377
screw gage 311
screw heads, proportions of
A. S. M. E 296-299
Machine screws, A. S. M. E., flat fil-
lister head 297
A. S. M. E., flat
head 298
A. S. M. E., oval fil-
lister head 296
A. S. M. E., round
head 299
A. S. M. E., special 294
A. S. M. E., stand-
ard 292
A. S.M.E., standard
proportions . . 290-299
diagram, A. S. M. E. 291
fillister head, Amer.
Screw Co 289
flat and round head,
Amer. Screw Co. 288
INDEX
665
PAGE
Machine screw taps 69-70
Machine screw taps, A. S. M. E 293
Machine screw taps, A. S. M. E.
special 295
Machine shop terms, dictionary of
564-656
Machine tools, dictionary of 565-656
Machine tools, power required by
436-440
Magnetic chucks 228
Magnetic chucks, use of 229
Manganese, properties of 458
Manila rope data 425
Manila rope, power transmission of 425
Mannheim gold 457
Manufacturers' standard cold
punched nuts 302
Manufacturers' standard heads for
machine bolts 282
Manufacturers' standard hot pressed
and forged nuts 301
Manufacturers' standard hot pressed
nuts 301
Manufacturers' standard narrow
gage nuts 303
Measures and weights, English. .470-471
Measuring Acme 29-deg. threads. ... 38
Brown & Sharpe worm
threads 39
Brown & Sharpe worm
threads, table of wires for 39
dovetails, external and in-
ternal 366
dovetails with plugs in
angles 366, 367
Measuring external screw-thread dia-
meters with micrometers and wires 29
Measuring fine pitch screw-thread
diameters 36
metric threads 37
60-deg. V-threads 32
60-deg. V-threads with
wires, table for 35
tapers 341
three-fluted tools with
micrometer 318
U. S. standard threads. . . 30
V-tools II
Whitworth screw threads 34
Whitworth screw threads
with wires, table for . . . 35
Melting points of metals 458
Melting points of solders 91
Mercury, properties of 458
Metal, bearing 456
Metal, slitting cutters, pitch of 192
Metals, chemical symbols for 458
Metals, fusible 456
Metals, properties of 458
Metals, specific gravity of 458
Metals, tensile strength of 458
Metals, weight of 458
Metric allowances for fits of all
classes 325
Metric and English conversion table 475
Metric pipe threads 45
Metric pitch gea^rs ii7
PAGE
Metric threads, measuring 37
Metric weights and measures 474-475
Micrometer graduations 318
Micrometer measuring of three-
fluted tools 318
Micrometer readings for U.S. threads 26
Micrometer readings for V-threads. . 27
Micrometer readings for Whitworth
threads 28
Micrometer, reading the 317
Micrometer, ten-thousandth 318
MilHmeters, decimal equivalents of
476-477
Millimeters, equivalent of inches in 478
Milhng and milling cutters 141-202
angles for indexing, table
190-191
cams by gearing up dividing
head 153
cams, heart-shaped 152
cutters, action of 142
fluting for 139-140
key ways for 199
number of teeth in
138-140
power required for . 144
side 147
spiral 143
spiral shell 146
T-slot 200
Milling indexing for cams 152
Milling, lubrication for 147
Milling machine indexing, plain and
differential 168-171
Milling machine indexing, tables for
plain and differential 172-189
Milling machine speeds and feeds. . . 141
Milhng machines, power required by 437
Milhng machine, universal, diagram
and parts of 621
Milling machine, table for cutting
spirals 148-151
Milhng machine, vertical, diagram
and parts of 623
Milling screw machine cams 155
Milling screw machine cams, tables
for 156-167
Milhng side teeth in milhng cutters 202
Milling squares on round stock 200
Milhng speeds and feeds 141
Mills, end, number of teeth m 138
Mills, hollow for screw machine . 246-247
Miter gear table. 123
Module, metric pitch 117
Morse tapers, short shank 35o-35i
Morse tapers, standard 348-349
Motors for cranes and hoists 439
Multiple threads, cutting 6
Multiple threads, face plate for 8
Muntz metal 457
Music wire sizes 4"
N
Narrow gage hot pressed nuts 303
Narrow gage washers 310
National standard hose coupling 50
666
INDEX
PAGE
Naval bearing metals 456
Nickel, properties of 458
Nonagon, properties of 525
Nurled-head jig screws 372
Nuts and bolt-heads, hexagonal,
Whitworth standard 303
Nuts and bolt-heads, stock required
for mfrs. standard 400
Nuts, automobile, A. L. A. M. stand-
ard 306
bolts and screws 279-315
castellated, for A. L. A. M.
standard bolts 306
check and jam, cold punched. 300
cold punched, mfrs. standard. 302
hot pressed and cold punched,
U. S. standard 300
hot pressed and forged, mfrs.
standard 301
hot-pressed, mfrs. standard,
he.xagon 301
hot pressed, narrow gage 303
planer 307
thumb 378
U. S. rough ..• 280
wing 377
O
Octagon bar steel, weight of 416
Octagon, properties of 528
Oilstones and their uses 241-244
Oilstones, artificial 241
Oilstones, care of 244
Oilstones, natural 241
Oilstones, shapes and sizes 241-242
Oval, countersunk head, cap screw,
flat end 287
Oval fillister head cap screws 286
Oval fillister head machine screws,
A. S. M. E. standard 296
P
Packfong 457
Parallel press and running fits
319, 320, 321
Patterns, estimating lumber in 403
Patterns, weight of castings propor-
tionate to 403
Penetration of carbon in caseharden-
ing.... 448
Penetration tests 449
Pennsylvania R. R. bearing metal. . 456
Pentagon, properties of 525
Perpendicidars, erection of, by tri-
angles 387
PickUng bath for cast iron 78
Pilots for counterbores, dimensions of 379
Pins and reamers, taper 357
Pins, cotter 309
Pins, taper 357
Pins, taper, drill sizes for 358
Pins, taper, U. S. ordnance 359
Pipe and pipe threads 42-50
Briggs standard, drill sizes for 45
die, Briggs standard 46
TPAGE
Pipe drills, sizes for 45
gages, Briggs standard 46
hobs, cutters for fluting 196
hobs, number of flutes 196
joints in Briggs system 46--
reamer for Briggs standard .... 46
tap for Briggs standard 46
taps, Briggs _. 73
taps, taper and straight, cutter
for fluting 196
thread gages, Briggs standard. . 49
threading speeds 68
threads, Briggs standard 4a
Briggs standard, table
of 47
British standard 44
metric •.•■•.••• 4S
Whitworth standard, drill sizes
for 45
Pitch line of gears 93
Planer, diagram and parts of 626-627
Planer head bolts and nuts 307
Planer nuts 307
Planers,^utting speeds ....... .\ .. . 399
Planer tools, various forms of. .•.651-^52
Planers, various types, power re-
quired by 436
Planing mill equipment, power re-
quired for. 440
Planks, board feet in pieces 402
Plates, steel, iron, brass and copper,
weights of 412-413
Platinum, properties of 458
Play of calipers, endwise in measuring
for press and shrink fits. 329
Play of calipers, sidewise in measur-
ing for running fits 329
Plug gage limits for standard holes 322
Plug gages, standard dimensions. . . . 380
Polishing wheels, care of 230
Polishing wheels, speed of 230
Polishing wheels, varieties of 220
Polygons, table of regular 525
Powder, diamond _ 234
Power required by machine tools
436-440
Power required for milling cutters . . 144
Power required for planing mill
equipment . .' 440
Power required for punching 441
Power required to remove metal. . . . 441
Pratt & Whitney key system siS
Press and running fits 319-331
Press fits for wheel hubs 327
Press fits, inclination of calipers in
measuring for 329
Press tools, lubricants for punch. . . . 272
Pressure angle of gear teeth 106
Prime-number fractions, table of 488
Properties of metals. 45S
Proportions of machine screw heads,
A. S. M. E. standard. . . 296
Protractor in screw cutting '. 6
Pulley, finding size of 527 •
Pulleys and gears, speeds of 43°. 43i
Punch and die, allowances for accu-
rate work 27Q
INDEX
667
PAGE
Punches and shears, power required
by 439
Punch and die boiler work, clearance
for 271
Punch and die, clearances for various
metals 271
Punching, power required for 441
Punch press dies, various types of
588-598
Punch press shells, finding diameters
of 266-267
Punch press shells, tables of diame-
ters 268-269
Punch press tools 266-272
Pyrometers, using for testing steel. . 452
Q
Quadruple thread cutting 7
Quenching steel, temperatures for . . . 452
R
Radial and thrust bearin^g^ com-
ickdial bearings. . ." 381
Radial bearings, self -aligning 386
Radial drill, diagram and parts of 601
Radius, finding without center 526
Rawhide, lubricants for 207
Reading the micrometer 317
Reading the ten-thousandth micro-
meter 318
Reading the vernier 316
Readings of screw thread micrometer
for U. S. threads 26
Readings of screw thread micrometer
for V-threads 27
Readings of screw thread micrometer
for Whitworth threads 28
Reamer and cutter grinding 237-239
Reamer clearance, grinding 237-239
Reamer for Briggs pipe 46
Reamer, number of flutes 197
Reamer, shell, cutters for fluting. . . . 197
Reamer, taper, number of flutes .... 198
Reamers, fluting cutters for 197-198
Reamers for dowel pins 64
Reamers, taper 357
Reamers, various types of . . . . . 630-632
Reaming speeds and feeds in screw
machine 264-265
Reciprocals of numbers, i to 1000
515-520
Reed tapers 354
Ring gages, standard dimensions ... 380
Riveted washers 311
Rivet heads, boiler 314
Rivet heads, tank 314
Rivets, round head, length of 315
Rolled steel, properties of 458
Rolled threads 23
Rolled thread screws, dimensions of
, U. S. S. blanks.... 23
Rope, data of Manila 425
Rope, Manila, power transmission of 425
Ropes and chains, safe loads'for .... 469
PAGE
Rose chucking reamer 198
Rotary cutting speeds in turning and
boring 206
Round bar stock, weight of 416-417
Round fillister head cap screws 286
Roimd head machine screws, A. S.
M. E 299
Round head rivets, length of 315
Rule, two-foot, angle obtained by
opening 403
Running and press fits 319-331
Running fits, clearances of 323
Running fits for power transmission
machinery 327
Running fits, side play of calipers for
328, 330
S. A. E. bolts and outs 306
horse-power rating 421
Sags of steel aUgning wire for shafting
428, 429
Saws, cold, power required by 438
Scales, fahrenheit and centigrade. . 455
Scleroscope hardness test 454
Screw, A.S.M. E., machine, diagram 291
Screw cutting, arrangement of gears 2
examples in i
gears for 3
multiple 6
rules for 3
Screw gage, machine and wood 311
Screw heads, proportions of A. S. M.
E. machine 296-299
Screw machine, allowance for thread-
ing 249
Screw machine box tools, finishing . 245
box tools, roughing. . 245
cams, tables for miU-
ing 156-167
counterboring speeds 265
cutters 245-246
cutting speeds for
brass 261
dies and taps 247
die sizes, spring 248
dimensions of cutters
forB. &S 256
drilling speeds and
feeds 264
feed chucks, harden-
ing 260
finish box-tool speeds
and feeds 262
forming tools, B. & S.
circular, tables of . 256-259
forming tools .... 251-259
hollow mills 246-247
hollow mills, dimen-
sions of 247
reaming speeds and
feeds 264, 26s
speeds and feeds for
different work. . 261-263
speeds and feeds for
forming tools 263
speeds and feeds for
screw stock 261
668
INDEX
PAGE
Screw Machine spring collets, harden-
ing 260
tapping speeds 265
taps, fluting cutters
for 195
length and
lands 249
number of teeth
in cutters. . . 195
threading, sizing work
for 248
threading speeds .... 265
tools, speeds and
feeds 245-265
tools, various forms
of 634, 635
Screw, test of lag 312
Screw-thread angles. .-. 4
Screw-thread diameters, measuring
external with micrometers and wires 29
Screw-thread lengths, coach and lag . . 312
Screw-thread micrometer caliper .... 28
Screw threads 1-38
Screw threads. Acme, 29 deg 24
Screw threads, British Association,
table of 19
Screw threads, cutting i
Screw threads, French (metric)
standard table of 20
Screw threads, German Loewenherz,
table of 22
Screw threads, International stand-
ard 21
Screw threads, sharp V, table of 17
Screw threads, U. S. standard, table
of 16
Screw threads, various forms of. .640-641
Screw threads, watch 33
Screw threads, Whitworth, measur-
ing 34
Screw threads, Whitworth, measur-
ing with wires, table for 35
Screw threads, Whitworth standard,
table of 18
Screws, automobile, A. L. A. M.
standard 306
bolts and nuts 279-315
button-head cap 287
cap, flat and oval counter-
sunk head 287
cap, hexagon and square
heads 284
coach and lag 312
collar head 285
fillister head cap 285
fillister head cap, flat, round
and oval 286
jig, binding , 371
collar-head /...'. 370
headless 37i
locking 371
nurled-head 372
square-head 371
supporting 371
winged 370
machine, A. S. M. E. flat
fillister head 297
PAGE
Screws, Machine, A. S. M. E. flat
head 298
A. S. M. E. oval
fillister head 296
A. S. M. E. round
head 299
A. S.M.E. special. ... 294
A. S. M. E. stand-
ard 292
A. S. M. E. stand-
ard proportions. 290-299
fiUister head, Amer.
Screw Co 289
flat and round head,
Amer. Screw Co . . . 288
rolled thread, U. S. S., di-
mensions of blanks 23
set, Hartford Mach. S. Co's
standard 283
standard threads per inch,
Amer. Screw Co 290
taps for A. S. M. E. machine 293
taps for A. S. M. E. special
machine 295
various types of 636-639
wood 313
Seamless tubing, weight of 419
Secants and co-secants, table of. 562-563
Sellers hob, cutter for fluting 196
Sellers tapers 356
Sellers hob taps 76
Set screws, Hartford Mach. S. Co's,
standard • 283
Shafting, ahgning by steel wire. . . 428
Shafting, horsepower and belts . . 420-443
Shafting, horsepower of steel 430
Shaper, diagram and parts of 643
Shapers, power required by 437
Sheet steel and iron, weights of, U.
S. standard gage 411
Shell blank diameters, tables of. .268-269
Shell blanks, finding diameter of
266-267
Shop and drawing room standards
369-404
Short shank tapers, Morse 350-351
Shot metal 457
Shrinkage of castings 458
Shrink fit allowances 322
Shrink fits, inclination of cahpers in
measuring for 329
Side milling cutters 147
Side play of calipers in boring holes 330
Side play of cahpers in measuring for
running fits 328, 330
Sides, angles and sines, tables of .392-397
Silver, properties of 458
Sines and co-sines, table of 540-551
Sines, sides and angles, tables of. 392-397
Single-end ball handles 376
Sizing work for screw machine
threading 248
Shdes and gibs, table for dimension-
ing 364, 36s
Slings for handling work 464-468
Soldering 86--92
Soldering aluminum 92
INDEX
669
PAGE
Soldering, cast iron 89
Soldering, cleaning and holding
work 89
Soldering, cold 9°
Soldering flaxes for various metals
86-87
Soldering, flux recipes 88
Solders and fusible alloys 9°
Solders, melting points of 91
Spacing bolt circles 523
Spacing holes in circles, table for. 390-391
Specific gravity of metals 4S8
Speculum 457
Speed of polishing and buffing wheels 230
Speed of twist driUs 53
Speed of wood turning 405
Speeds and feeds for brass in screw
machines 261
Speeds and feeds for drills in screw
machine 264
Speeds and feeds for forming tool,
screw machine 263
Speeds and feeds for gear cutting. . . 140
Speeds and feeds for milling ma-
chines 141
Speeds and feeds for reaming in screw
machine 264-265
Speeds and feeds for screw-machine
drilling 264
Speeds and feeds for screw-machine
finish box tools 262
Speeds and feeds for screw-machine
work 261-265
Speeds and feeds for screw stock,
table of 261
Speeds, circumferential, tables of .431-437
Speeds of cold-saw cutting-off ma-
chines 203
Speeds for counterboring in screw
machine 265
Speeds for tapping and threading ... 68
Speeds for threading in screw ma-
chine 265
Speeds of belts 424
Speeds of grinding wheels, table .... 220
Speeds of planers, cutting 399
Speeds of pulleys and gears .... 430, 431
Speeds of tapping in screw machines 265
Speeds, rotary cutting in turning and
boring 206
Spindles for grinding wheels, sizes. . . 227
Spiral gears 134
Spiral gears, spur gear cutters for. ... 136
Spiral gears, table of real pitches 132-133
Spiral shell cutters 146
Spirals, table for cutting on milling
machine 148-150
Spline fittings, automobile, broaches
for 277-278
Spring cotters 309
Spring die sizes, screw machine. ... 248
Spring dies, sizes of 248
Sprocket wheels 118-119
Spur gears, laying out blanks 103
Square bar stock, weight of 416-417
Square corner, laying out 405
Square countersunk head bolts 305
PAGE
Square-head cap screws 284
Square-head jig screws 371
Square, properties of 528
Squares, cubes and roots of numbers,
I to 1000 492—501
Squares, largest milled on round
stock 200
Squares of numbers, tables of . . . 488-489
Square thread taps 77
Square washers, standard sizes 310
Standard jig parts 369-372
Standard Tool Go's short taper,
standard 353
Standard Tool Go's taper shanks,
standard 352
Stationary bushings for jigs. . . . 369, 370
Steam engine horse-power 420
Steam hammers and drop forging
460-463
Steam hammers, capacities 460
Steel and iron, sheet, U. S. standard
gage weights 411
Steel and other metals 444-459
anneaUng 446
bars, weight per linear foot. . . 416
carbonizing, rate of penetration
448, 449, 450
casehardening 448
cast, properties of 458
composition and hardening
effects 451
flat sizes, weight of 418
hardness test, Brinell 452, 453
hardness test, scleroscope 454
harveyizing 448
heat treatment of 444-447
high-speed 447
plates, weights of . 412-413
properties when annealed 451
properties when hardened .... 451
rolled, properties of 458
shafting, horse-power of 430
tempering 447
wire and twist-drill gage sizes
406-408
gage sizes 406
Stubs' sizes and weights. 410
weights of 414-415
Stock allowed for upsets 399
Stock flat sizes, steel, weight of 418
Stock sheet brass, copper, steel and
wire, weight of 411-415
Stock required for bolt-heads and
nuts, mfrs. standard 400
Stock required for bolt-heads and
nuts, U. S. standard 401
Stock weights and wire gages . .406-419
Stove bolt diameters and threads . . . 305
Stove bolt taps 74
Straight keys, dimensions 333
Straps, jig 372
Stubs' gages, wire 406
Stubs' steel wire sizes and weights. . 410
Stub tooth gears 107
Studs, depths to drill and tap for 308
Supporting jig screws 371
Symbols, chemical of metals 458
670
INDEX
T
PAGE
Tangents and co-tangents, table of
S3Q-S40
Tank rivet heads 314
Tap bolts , 30s
drills for S. A. E. threads 62
for double depth threads . 65
for machine screw taps. . . 63
for pipe taps 45
for regular threads 62
for V-thread taps 66
threads, Acme 29 deg 25
for Briggs standard pipe 46
lengths and lands, screw ma-
chine 249
screw machine, lengths and
lands of 249
Taper gage, applications of 342
accurate 341
applications of formulas
for using . .._. 343-345
formulas for using 343
pin drill sizes 3S8
pins and reamers 357
pins, U. S. ordnance 3SQ
reamers, number of flutes .... 198
shanks, Standard Tool Go's
standard 352
taps, die 75
Tapers and dovetails 341-367
B. & S. standard 34^-347
for keys 340
Jamo 355
per foot and corresponding
angles table of 361
Morse standard 348-340
Reed 354
Sellers 356
short shank, Morse 350-351
short. Standard Took Go's
standard 353
table for computing 362-364
table of lengths up to 24-in. . 360
Tappers, nut, power required by 438
Tapper taps 72
Tapping for studs, depth of 308
Tapping speeds 67
Tapping speeds in screw machine 265
Taps and dies for screw machine cut-
ters for fluting 195-196
Taps, Briggs pipe 73
for A. S. M. E. special screws 295
for machine screws, A. S. M. E.
standard 293
hand : 71
hand, cutters for fluting 195
hand cutters, number of teeth
in 19s
hob, cutters for fluting 196
hob, number of flutes 196
machine screw 69-70
screw machine, fluting cutters
for 19s
screw machine, number of
teeth in cutters I95
Sellers hob 76
square thread 77
PAGE
Taps, stove bolt 74
taper die 75
tapper 72
tapper cutters for, number of
teeth in 195
tapper, fluting cutters for ... . 195
various types of 648
Tempering steel 447
Terms, machine shop, dictionary of
565-656
Test for lag screws 312
Thermometers, Fahr. and Gent 455
Thread angle table 4, 5
Thread cutting, arrangement of
gears for 2
depth table 65
fractional i
multiple 6
multiple, face plate
for 8
rules for 3
Thread lengths on coach and lag
screws 312
Thread micrometer readings for U.
S. thread 26
Thread micrometer readings for
V-thread 27
Thread micrometer readings for
Whitworth threads 28
Thread tool, grinding flat on U. S.
form 14, IS
Thread tools, grinding flat on 13
Thread tools, measuring 12
Threading in screw machine, sizing
work for 248
Threading machines, pipe, power re-
quired by 438
Threading speeds 68
Threading speeds in screw machine 265
Threads, Acme 29-deg. screw and
tap, wires for measuring. 38
angle of screw 4
Briggs pipe, table of 47
British Association screw,
table of ■ 19
Brown & Sharpe 29-deg.
worm, table of 39
Brown & Sharpe worm and
Acme compared 10
Brown & Sharpe worm,
measuring 39
cutting screw i
fine pitch screw, measuring
diameters 36
French (metric) standard
screw, table of 20
German Loewenherz, table
of 22
International standard screw,
table of 21
metric, measuring 37
metric pipe 45
of special diameter, measur-
ing 29
per inch, Amer. Screw Go's
standard 290
pipe 42-50
INDEX
671
PAGE
Threads, pipe, Briggs standard 42
pipe, British standard 44
rolled 23
rolled screw, dimensions of
U. S. S. blanks 23
screw 1-38
screw. Acme, 29 deg 24
screw, various forms of 640-641
sharp V screw, table of.
69-deg. V, measuring
60-deg. V, measuring with
wires, table for
table of U. S. standard
34
screw
tap. Acme, 29 deg
29-deg. Acme, measuring . .
U. S. standard, measuring.
U. S. standard, measuring
with micrometers and
wires, table of
watch screw . .'
Whitworth screw, measur-
ing
Whitworth screw, measur-
ing with wires, table for. 35
Whitworth standard screw,
table of 18
worm, wire sizes for measur-
ing Brown & Sharpe,
table of 39
Three-fluted tools, measuring with
micrometer 318
Thrust bearings, collar 382, 383
Thumb nuts 3 78
Tin, properties of 458
Tools, lathe and planer, various
forms of 650
Tools, measurement of V 11
Triangle, properties of 527
Triangles, right-angled, integral 387
Trigonometry, shop 521-528
Triple threads, cutting 7
T-slot bolt heads, standard 308
T-slots in milling cutters 200
Tubes, Briggs standard, table of . . . . 43
Tubing, seamless brass, weight of . . . 419
Tungsten, properties of 458
Turning and boring 205-207
Turning and boring, formula for
machining time 206
Turning and boring, table of cutting
time 205
Twist drill gage sizes 406
Twist drills 51-66
angle of spiral 51
blacksmith 56
clearance angle 52
feed of 53-54
grinding and sharpening 52
groove shapes 51
hollow 56
letter sizes 60
oil 56
pointers on 55
ratchet 55
shell 55
sizes of 58-61
PAGB
Twist drills, speed of 53
straightway or formers. 56
troubles 55
types of 56-57
wire 56
Type metal 457
Types, making in drop-forge dies. 462, 463
U
Undecagon, properties of 525
Upsets and bolt heads, allowances for 399
United States bolts and nuts, finished
heads and nuts 281
United States bolts and nuts 279-282
United States bolts and nuts, rough . 280
I United States bolts and nuts,
strength of 279
United States form of thread, grind-
ing flats on tools for 14, 15
United States hot pressed and cold
punched nuts 300
United States ordnance taper pins . . 359
United States standard bolt-heads
and nuts, stock required for 401
United States standard gage for
plate, weights of 411
United States standard screw
threads, table of 16
United States standard threads,
measuring 30
United States; standard threads,
measuring with micrometers and
wires, table for 31
United States standard washers 310
United States threads, micrometer
readings for 26
Vanadium, properties of 458
V-block, used with micrometer 319
Vernier graduations 316
Vernier, how to read 316
Vernier scales, principles of 317
Versed sine of angle 525
Volume of fillets, table of 404
V-screw threads, table of sharp 17
V-thread, finding depth of 522
V-thread, micrometer readings for. . . 27
V-threads, 60-deg., measuring 32
V-threads, 60-deg., measuring with
wires, table for 33
V-toob, measurement of 11
W
Washburn and Moen music wire
sizes 411
Washburn and Moen wire gage sizes 407
Washers, cast iron 311
Washers, for planer bolt heads 307
Washers, narrow gage 310
Washers, riveted 311
Washers, square, standard sizes 31Q
672
INDEX
PAGE
Washers, U. S. standard 310
Watch screw threads 33
Water conversion factors .......... 473
Webster and Horsefall music wire
sizes 411
Weight of brass, copper and alumi-
num bars per linear foot 417
Weight of castings in proportion to
patterns 403
Weight of fillets, table of 404
Weight of flat sizes of steel 418
Weight of patterns 403
Weight of seamless brass tubing .... 419
Weight of steel and iron bars per
linear foot 416
Weight of steel, iron, brass and cop-
per plates 41 2-413
Weight of steel, iron, brass and cop-
per wire 414-415
Weight of steel wire. Stubs' gage . . . 410
Weight of substances, table of
471-473
Weights and measures, English. .470-471
Weights and measures, metric. . 474. 475
Weights of stock 406-419
Wheels, grinding {See Grinding)
Wheels, hand, dimensions of 373
White metal 457
Whitney keys and cutters 336
Whitworth screw threads, measuring 34
Whitworth screw threads, measuring
with wires, table for 35
Whitworth standard nuts and bolt-
heads, hexagonal 303
Whitworth standard screw threads,
table of 18
Whitworth threads, micrometer read-
ings for 28
Width of belts 424
Winged jig screws 37°
Wing nuts 377
Wire and drill sizes arranged con-
secutively 408-409
PAGE
Wire gage dimensions in decimal
parts of an inch 407
Wire gages and stock weights . . . 406-419
Wire gages. Stubs' 406
Wire gage sizes, twist-drill and steel
406-408
Wires for measuring Brown & Sharpe
worm threads 39
Wire sizes and weights, Stubs' steel. 410
Wire, sizes of music 411
Wires, measuring Acme 29-deg. screw
and tap threads with 38
Wire, steel, aligning shafting by. . . . 428
Wire, steel, iron, brass and copper,
weights of 414-415
Woodruff keys 336
Wood screw gage 311
Wood screws 313
Wood turning, speed of 405
Work benches, construction of 84
Work benches, hight of 86
Work benches, material for 85
Worm gearing 137
Worms, cutting diametral pitch .... 8
Worm thread, Brown & Sharpe and
Acme screw thread compared 10
Worm thread proportions for worm-
wheels 139
Worm threads, Brown & Sharpe,
measuring 39
Worm threads, finding pitch diame-
ters of 138
Worm threads, 29-deg. Brown &
Sharpe, table of 38
Worm threads, wire sizes for measur-
ing Brown & Sharpe 39
Worm wheel hobs 41
Wrenches, various types of 655-656
Wrought iron, properties of 458
Z
Zinc, properties of 458
LIST OF AUTHORITIES
Acme Machinery Co 399
Alford, L. P 64
Almond, R. A 13-15
American Screw Co 69, 288, 289
American Swiss File & Tool Co 83
Armes, F. W 456
Atkins, H. F 11-13
Badge, F. J 461
Baker Bros 33i>332
Baldwin Locomotive Works 271
Bardons & Oliver 137
Beale, O. J. (Jarno) 355
Becker Milling Machine Co 124
Bignall & Keeler Mfg. Co 68
Bird, W. W 422
Blake, H. F 90
Boston Elevated Railroad 327
Brown & Sharpe Mfg. Co 10, 11, 26,
27, 28, 38, 39, 41, 104, 141,
203, 218, 275, 324, 346
Brownstein, Benj 404
Cantello, Walter 11, 28-33, 35. 39
Carborundum Co 211
Carstensen, Fred 152
Cheetham, J. H 67
Cincinnati Gear Cutting Machine Co. 140
Cincinnati Planer Co 399
Cincirmati Milling Machine Co.. 142,
145, 147, 155, 237
Clamer, G. H 456
Cleveland Twist Drill Co 51
Colbum, A. L 4-6
Cook, Asa 109
Corbin Screw Corporation 290
Cregar, J. W 86
Dangerfield, Jamies — :■.'■ 36
Darbyshire, H 209-216
Dean, C 270-271
De Leeuw, A. L\^,.^.. .>..v ^v '- 142
Dilloway, W. T ' :.... 368
Disston & Sons, Henry 72
Dodge Mfg. Co 327
Ellis, M. E 369-372
Ermold, E. A 274
Fellows Gear Shaper Co 107
Eraser, Jas 201
Gardner, Wm. R 205
Gates, Grandon iii
General Electric Co 322
Goodrich, C. L 245-265
Halsey, F. A 137
Hartford Machine Screw Co 283
Haughton, Wm 131
Haskell Mfg. Co., Wm. H 304
Hedglon, M. J 374
PAGE
Herbert, Edward G 82
Hess-Bright Mfg. Co 381, 382
Hoagland, F. O 318
Hobart, Jas. F 426, 427
Holz, Fred 141-143, 237-239
Hoopes and Townsend. . . .282, 304, 312
Hunt Co., C. W 319
Johnson, E. A 231-234
Jones & Laughlin 333
Josslyn, C. E 191
Kearney, E. J 127
Kelly, S. J 207
Lachman, Robt 200
Lake, E. F 444
Lamb, Harold 202
Landis Machine Co 68
Landis Tool Co 217
Logue, C. H 129
McAlpine, Arthur 398
MacArthur, C. P 269
Miller, C. A 255
Milton Mfg. Co 310, 311
Morse Twist Drill and Machine Co . 349
National Machine Co 68
National Machinery Co 282, 400
Newall Engineering Co. . . . 322, 325, 326
New Britain Machine Co 84
New Departure Mfg. Co 384
Newton Machine Tool Works 203
Niles-Bement-Pond Co 460
Norse, A. H 428
Norton Co 209, 211, 227
Noyes, H. F 364-365
Nuttall Co 108
Oke, A. Livingstone 464
Pike Mfg. Co 241
Pomeroy, L. R 441
Pratt & Whitney Co 49, 285, 335,
357, 373, 375
Press, A. P 272
Rantsch, E.J 8-10
Reed & Prince Mfg. Co 23
Reed Co., F. E 354
Ryder, T 8
Robbins, Chas 443
Safety Emery Wheel Co 222
Scribner, F. C 37
Seidensticker, F. W 393-397
Sellers & Co., Wm 107, 357
Shore, A. F 454
S. K. F. BaU Bearing Co 386
Stabel, Jos 380
Standard Engineering Co 68
Standard Steel Gage Co 337
Standard Tool Co 352. 353
673
674
LIST OF AUTHORITIES
PAGE
Stutz, C. C 341
Sweet, John E 52
Tindel-Morris Co 203
Trebert, A 6-7
Trenton Iron Co 407
Tryon, W. L 431
Upson Nut Co 304
Valentine, A. L 192-199
Vernon, P. V 331
Walcott & Wood Machine Tool Co. . 376
PAGE
Waltham Watch Co 33
Washburn & Moen Mfg. Co 407-411
Webster & Horsefall 411
Wells & Sons Co., F. E 60
Wells Bros. Co 70, 71-74
Welsh, T. E 366, 367
Whitney Mfg. Co 336, 337
Winslow, B. E 402
Woodworth, J. V. . 272, 589-593, 597, 598
Zeh, E. W 266
<k ^.i .
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Friction Clutches.
Cams.
Springs.
Bolts, Nuts, and Screws.
Wire and Sheet Metal
Pipe and Pipe Joints.
Minor Machine Parts.
Press and Running Fits.
Balancing Machine Part§.
Miscellaneous Mechanisms, Con-
structions and Data.
Performance and Power Require-
ments of Tools.
Cast Iron.
Steel.
Alloys.
Weights of Materials.
Heat.
Steam Boilers.
Steam Engine.
Gas Engine.
Compressed Air.
Mechanics.
Strength of Machine Parts.
Weights and Measures.
Hydraulics and Hydraulic Machinery. Mathematical Tables.
McGRAW-HILL BOOK COMPANY, Inc.
239 WEST 39th STREET
NEW YORK
London
Berlin
Mechanical Engineers'
Handbook
LIONEL S. MARKS, Editor-in-Chief
Professor of Mechanical Engineering, Harvard University and
Massachusetts Institute of Technology
ASSISTED BY OVER 50 SPECIALISTS
PUBLISHED JUNE, 1916
Total Issue 30,000
'T^HIS handbook is the standard today wherever mechan-
-■- ical engineering data are used.
It is an encyclopedia of mechanical engineering compiled
by over 50 widely known specialists. Their names are
guarantees of the quality, usefulness and accuracy of these
data.
The book's noteworthy characteristics are:
1. Each subject is treated by a specialist and
is authoritative in character.
2. Fundamental theory is thoroughly covered.
3. The engineering data have been selected
discriminatingly by a specialist instead of
leaving the reader to select from conflicting
data.
The book is arranged and indexed for quick reference.
In addition to thumb indexes for the major topics there are
quick reference indices on the inside of the front and back
covers and on the fly leaves of the 15 sections. There is
also a big general index at the end comprising more than
7000 references.
If you need mechanical engineering data at all, you need
Marks.
1,800 pages, pocket size, flexible binding, thumb indexed,
$5.00 net, postpaid
SOUTHEASTERN MASSACHUSETTS UNIVERSITY
SPECIAL COLL TJ1165.C65 1914
American machinists' handbook and dictio
3 ETE5 0D113 7fi7 3
SPECIAL COLL TJ 1165 .C65 1
Colvin, Fred Herbert (Fred
Herbert) 1867-1965
American machinists'
handbook and dictionaxv^ of
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